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1. HeiDOK 03D75 Abstract and axiomatic computability and recursion theory ( 0 Dok. ) 03D80 Applications of computability and recursion theory ( 0 Dok. http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03D&anzahl

2. FOM: CTA Meeting; Applications; Nabutovsky-Weinberger If we are going to compile lists of ``Applications of recursion theory, . discussion of issues and programs in recursion theory / computability theory. http://cs.nyu.edu/pipermail/fom/1999-July/003246.html

FOM: CTA meeting; applications; Nabutovsky-Weinberger Stephen G Simpson simpson at math.psu.edu Thu Jul 15 22:33:53 EDT 1999 Previous message: FOM: 48:Continuous Embeddings/Reverse Mathematics Next message: FOM: Some Problems in Reverse Mathematics Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... http://www.cs.uchicago.edu/~soare/lectures/geometry.html Previous message: FOM: 48:Continuous Embeddings/Reverse Mathematics Next message: FOM: Some Problems in Reverse Mathematics Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

3. Richard A. Shore: Curriculum Vitae Survey Lecture, 2nd Symposium on Generalized recursion theory, Oslo, June 1977. 20minute Talk, Special Session on computability theory and Applications http://www.math.cornell.edu/~shore/vitae.html

Richard A. Shore : Curriculum Vitae Education Employment Invited Talks Grants ... Publications Education A. B. Summa cum laude in Mathematics, Harvard University, 1968. Ph.D. in Mathematics, M.I.T., 1972. Employment M.I.T., Teaching Assistant, 9/68-6/72. University of Chicago, Instructor, 10/72-9/74. Cornell University, Assistant Prof., 7/74-6/78; Associate Prof., 7/78-3/83; Prof., 4/83-. University of Illinois, Chicago, Assistant Professor, 1/77-8/77. University of Connecticut, Storrs, Visiting Associate Professor, 9/79-12/79. M.I.T., Visiting Associate Professor, 1/80-5/80. Hebrew University of Jerusalem, Visiting Professor, 9/82-6/83. University of Chicago, Visiting Professor, 2/87. University of Sienna, Italy, Visiting Professor, 5/87. MSRI, Berkeley, Member, 1989-1990. Harvard University, Visiting Scholar, 1/97-6/97. M.I.T., Visiting Scholar, 1/97-6/97. National University of Singapore, Distinguished Visiting Professor, 12/99-1/00. Harvard University, Visiting Scholar, 1/02-7/02. Invited Talks Survey Lecture, Annual Meeting of the Assoc. for Symbolic Logic, Washington, D.C., January 1975. 20-minute talk, Special Session on Recursively Enumerable Sets and Degrees, AMS, Toronto, August 1976.

4. 03Dxx 03D65 Highertype and set recursion theory; 03D70 Inductive definability and recursion theory; 03D80 Applications of computability and recursion theory http://www.ams.org/msc/03Dxx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Computability and recursion theory 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions [See also 03D10 Turing machines and related notions [See also 03D15 Complexity of computation [See also 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively (computably) enumerable sets and degrees 03D28 Other Turing degree structures 03D30 Other degrees and reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40 Word problems, etc. [See also 03D45 Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D80 Applications of computability and recursion theory 03D99 None of the above, but in this section

5. Mhb03.htm 03D80, Applications of computability and recursion theory. 03D99, None of the above, but in this section. 03Exx, Set theory. 03E02, Partition relations http://www.mi.imati.cnr.it/~alberto/mhb03.htm

03-XX Mathematical logic and foundations General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. General logic Classical propositional logic Classical first-order logic Higher-order logic and type theory Subsystems of classical logic (including intuitionistic logic) Abstract deductive systems Decidability of theories and sets of sentences [See also Foundations of classical theories (including reverse mathematics) [See also Mechanization of proofs and logical operations [See also Combinatory logic and lambda-calculus [See also Logic of knowledge and belief Temporal logic ; for temporal logic, see ; for provability logic, see also Probability and inductive logic [See also Many-valued logic Fuzzy logic; logic of vagueness [See also Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

6. 03Dxx 03D70, Inductive definability. 03D75, Abstract and axiomatic computability and recursion theory. 03D80, Applications of computability and recursion theory http://www.impan.gov.pl/MSC2000/03Dxx.html

Computability and recursion theory Thue and Post systems, etc. Automata and formal grammars in connection with logical questions [See also Turing machines and related notions [See also Complexity of computation [See also Recursive functions and relations, subrecursive hierarchies Recursively (computably) enumerable sets and degrees Other Turing degree structures Other degrees and reducibilities Undecidability and degrees of sets of sentences Word problems, etc. [See also Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see Recursive equivalence types of sets and structures, isols Hierarchies Computability and recursion theory on ordinals, admissible sets, etc. Higher-type and set recursion theory Inductive definability Abstract and axiomatic computability and recursion theory Applications of computability and recursion theory None of the above, but in this section

7. Research Areas Rebecca Weber, My research focuses on computability (recursion) theory. and its Applications to computational biology and to other fields. http://www.math.dartmouth.edu/people/faculty/research/index.phtml?s=RPR

8. Harizanov Home Graduate topics computability theory and Applications to structures; .. copies of a computable relation,” International Workshop on recursion theory and http://home.gwu.edu/~harizanv/

Valentina S. Harizanov Office Government Hall (2115 G Street), Room 220 Phone e-mail: harizanv@gwu.edu Professor of Mathematics Columbian College of Arts and Sciences GWU Curriculum Vitae pdf Office hours at other times by appointment any time by e-mail Teaching Current Courses Previous Courses Other Courses Taught at GW Teaching Evaluations ... Doctoral Students Research Research Interests Research Publications in Refereed Journals Recent and Future Meetings Books ... Special Lectures at GWU Other Graduate Education Professional Affiliations Translations Invited Book Reviews ... Web Pages of Recent Co-Authors Research Interests Most of my research is in computable recursive algebra and model theory (see Harizanov's Handbook of Recursive Mathematics chapter) and in computability recursion theory , which are subfields of mathematical logic (see Crossley's 2005 tutorial ). I am especially interested in computability theoretic complexity of relations (see Hirschfeldt's Bulletin of Symbolic Logic paper ) and structures (see Harizanov's Bulletin of Symbolic Logic paper ), including their Turing degrees. Computability theory is the mathematical theory of algorithms. Problems which can be solved algorithmically are called decidable. Undecidable problems can be more precisely classified by considering generalized algorithms, which require external knowledge. Turing degrees provide an important measure of the level of such knowledge needed. (See

9. ScienceDirect - Theoretical Computer Science : Effectively Closed Sets And Graph In this paper, we compare the computability and complexity of a continuous real . A. Nerode, W. Huang, Applications of pure recursion theory to recursive http://linkinghub.elsevier.com/retrieve/pii/S030439750100069X

Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page Theoretical Computer Science Volume 284, Issue 2 , 28 July 2002, Pages 279-318 Abstract Full Text + Links PDF (312 K) Related Articles in ScienceDirect Hierarchies of Function Classes Defined by the First Va... Electronic Notes in Theoretical Computer Science Hierarchies of Function Classes Defined by the First Value Operator: (Extended Abstract) Electronic Notes in Theoretical Computer Science Volume 120 3 February 2005 Pages 59-72 Armin Hemmerling Abstract The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy connected with Ershov's one within . The non-effective version over real functions is connected with the degrees of discontinuity and yields a hierarchy related to Hausdorff's difference hierarchy in the Borel class . Finally, the effective version over approximately computable real functions forms a hierarchy which provides a useful tool in computable analysis.

10. Cenzer, Douglas computability theory and its Applications (Boulder, CO, 1999), 3959, Contemp. Math., 257, recursion theory and complexity (Kazan, 1997), 1553, http://www.math.ufl.edu/fac/facmr/Cenzer.html

Cenzer, Douglas 58 papers Brodhead, Paul(1-FL); Cenzer, Douglas(1-FL); Remmel, Jeffrey B.(1-UCSD) Random continuous functions. (English summary) Proceedings of the Third International Conference on Computability and Complexity in Analysis (CCA 2006), 275287 (electronic), Electron. Notes Theor. Comput. Sci., 167, Elsevier, Amsterdam, Brodhead, Paul(1-FL); Cenzer, Douglas(1-FL); Remmel, Jeffrey B.(1-UCSD) Random continuous functions. (English summary) Proceedings of the Third International Conference on Computability and Complexity in Analysis (CCA 2006), 275287 (electronic), Electron. Notes Theor. Comput. Sci., 167, Elsevier, Amsterdam, Proceedings of the Third International Conference on Computability and Complexity in Analysis (CCA 2006). Held at the University of Florida, Gainesville, FL, November 15, 2006. Edited by D. Cenzer, R. Dillhage, T. Grubba and K. Weihrauch. Electronic Notes in Theoretical Computer Science, 167. Elsevier Science B.V., Amsterdam, 2007. front matter+447 pp. (electronic). Cenzer, Douglas(1-FL); Remmel, Jeffrey B.(1-UCSD)

11. JSTOR Computability In Combinatory Spaces. An Algebraic Chapter III defines the notion of relative computability in iterative combinatory spaces and studies the properties of the underlying recursion theory. http://links.jstor.org/sici?sici=0022-4812(199506)60:2<695:CICSAA>2.0.CO;2-#

12. Program On Computation Prospects Of Infinity - IMS computabilitytheoretic and proof-theoretic aspects of Vaughtian model theory Open Forum Future on recursion theory. Tuesday, 2 Aug 2005 http://www.ims.nus.edu.sg/Programs/infinity/activities2.htm

13. Logic, 8 Applications of firstorder logic dense linear orders, fields. Model theory is the art recursion theory – compare this to Sipser’s Computation, Part II http://www.media.mit.edu/physics/pedagogy/babbage/texts/rt.html

Introduction to Logic and Recursion Theory This is a transcription of relevant notes from the class 18.511 taught by Prof. Sacks in the Spring of 1998, organized and reinterpreted. Homework problems starting with problem 9 are solved in vitro. Notation is indecipherable. Propositional Calculus Propositional calculus is an example of a formal system . One must specify atomic symbols , which consist of letters A n , or symbols, and connectives expression is a finite sequence of atomic symbols. The set of well-formed formulas (WFFs) is defined recursively as follows: (A n g). This lets up build up new propositions from old ones. They are associative, etc. in the commonly held sense of these notions. A truth valuation c to the set of all WFFs, simply given by defining it recursively in the obvious fashion. Two WFFs are semantically equivalent disjunctive normal form semantically complete . It is obvious that we cannot discard the ! symbol, but one can combine the two to make the NAND operator, which is, all by itself, semantically complete, the Schaeffer stroke . In quantum logic, the CNOT is semantically complete, combined with an arbitrary unitary operator.

14. Computability Of Simple Games: A Characterization And Application To The Core - computability of simple games A characterization and application to the core . Classical recursion theory The theory of Functions http://mpra.ub.uni-muenchen.de/437/

@import url(http://mpra.ub.uni-muenchen.de/style/auto.css); @import url(http://mpra.ub.uni-muenchen.de/style/print.css); Munich Personal RePEc Archive Home Browse Search About ... Create Account Computability of simple games: A characterization and application to the core Kumabe, Masahiro and Mihara, H. Reiju Computability of simple games: A characterization and application to the core. Unpublished. There is a more recent version of this eprint available. Click here to view it. Full text available as: Preview PDF - Requires a PDF viewer such as GSview Xpdf or Adobe Acrobat Reader Abstract It was shown earlier that the class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games, strengthens the earlier result that computable games violate anonymity, and gives examples showing that the above inclusions are strict. It also extends Nakamura’s theorem about the nonemptyness of the core and shows that computable simple games have a finite Nakamura number, implying that the number of alternatives that the players can deal with rationally is restricted. Item Type: MPRA Paper Additional Information: Language: English Keywords: Voting games; infinitely many players; recursion theory; Turingcomputability; computable manuals and contracts

15. Education, Master Class 1988/1999, MRI Nijmegen Type theory and Applications H. Barendregt, E. Barendsen Prerequisites Basic recursion theory (characterisation of computable functions, http://www.math.uu.nl/mri/education/course_9899.html

Education, Master Class, Master Class 1998/1999, Detailed Course Content Detailed Content of the Courses Course content 1st semester: Model Theory W. Veldman Lambda Calculus H. Barendregt, E. Barendsen Recursion Theory and Proof Theory H. Schellinx Logic Panorama seminar 2nd semester: Type Theory and Applications H. Barendregt, E. Barendsen Incompleteness Theorems J. van Oosten Sheaves and Logics I. Moerdijk Mathematical Logic seminar Courses Name of the course: Model Theory Lecturer: W. Veldman Prerequisites: Some familiarity with mathematical reasoning. Literature: C.C. Chang, H.J. Keisler, Model Theory, North Holland Publ. Co. 1977 W. Hodges, Model Theory, Cambridge UP, 1993 Contents: Model theory studies the variety of mathematical structures that satisfy given formal theory. It may also be described as a study of mathematical structures from the logician's point of view. Model theory at its best is a delightful blend of abstract and concrete reasoning. Among the topics to be treated in this course are Fraisse's characterisation of the notion 'elementary equivalence' (structures A,B are called elementarily equivalent if they satisfy the same first-order-sentences), the compactness theorem and its many consequences, ultraproducts, some non-standard-analysis, Tarski's decision method for the field of real numbers by quantifier elimination and Robinson's notion of model completeness. If time permits, some attention will be given to constructive and recursive model theory.

16. Classes Since 2001 Fall 2007 M781 Coalgebra Coalgebra Is A Field recursion theory is the mathematical study of computability. course will go into detail on one of the main Applications of recursion theory in logic, http://www.indiana.edu/~iulg/moss/classes.htm

Classes since 2001 Fall 2007 M781: Coalgebra Coalgebra is a field of study which aims to study the general properties of a great variety of state-based dynamical systems, like transition systems, automata, process calculi, Markov chains, etc. These all can be captured uniformly as coalgebras, and coalgebra aims to be the mathematics of computational dynamics. Coalgebra is developing into a field of its own interest presenting a deep mathematical foundation, a growing field of applications and interactions with various other fields such as formal system specification, modal logic, dynamical systems, control systems, category theory, set theory, algebra, analysis, enumerative combinatorics, recursive program schemes, circularity, etc. The field as a whole is fairly new, and it is currently very active. Fall 2007 COLL-S 105: Freshman Seminar in Computability and Logic The theory of computation is one of the most important intellectual developments of the first half of the twentieth century. From very slender roots, a tree blossomed in the 1930's whose fruit is the development of computers as we know them. But the same tree contains thorns, as it were; these are the 'negative results' which talk about computer programs that we can never write, and true sentences which we can never prove. These results are often taken to imply fundamental limitations on what human beings can know. They are on a cultural par with other developments that came at roughly the same time: the uncertainty principle in physics, and even with Freud's notion of an unconscious which cannot know itself.

17. Recursion Theory And Joy Many topics from the theory of computability are particularly easy to handle within Joy. They include the parameterisation theorem, the recursion theorem http://www.latrobe.edu.au/philosophy/phimvt/joy/j05cmp.html

Global Utilities La Trobe Home Skip to Content Contact La Trobe Sitemap Search: Global Navigation About La Trobe Campuses Faculties Research ... International You are here: University home Philosophy Program Home page for Manfred von Thun Recursion Theory and Joy TITLE>Recursion Theory and Joy Recursion Theory and Joy by Manfred von Thun Abstract: Joy is a functional programming language which is not based on the application of functions to arguments but on the composition of functions. Many topics from the theory of computability are particularly easy to handle within Joy. They include the parameterisation theorem, the recursion theorem and Rice's theorem. Since programs are data, it is possible to define a Y-combinator for recursion and several variants. It follows that there are self-reproducing and self-describing programs in Joy. Practical programs can be written without recursive definitions by using several general purpose recursion combinators which are more intuitive and more efficient than the classical ones. Keywords: functional programming, functionals, computability, diagonalisation, program = data, diagonalisation, self-reproducing and self-describing programs, hierarchy of recursion combinators, elimination of recursive definitions.

18. Publications By Carl G. Jockusch Array nonrecursive sets and genericity (with R. Downey and M. Stob), computability, Enumerability, Unsolvability Directions in recursion theory, http://www.math.uiuc.edu/~jockusch/pubs.html

Publications by Carl G. Jockusch Semirecursive sets and positive reducibility, Trans. Amer. Math. Soc. Supplement to Boone's "Algebraic systems", in Contributions to Mathematical Logic Uniformly introreducible sets, J. Symbolic Logic The degrees of bi-immune sets, Z. Math. Logik Grundlagen Math. Countable retracing functions and P predicates (with T. G. McLaughlin), Pacific J. Math. Relationships between reducibilities, Trans. Amer. Math. Soc. The degrees of hyperhyperimmune sets, J. Symbolic Logic Minimal covers and arithmetical sets (with Robert I. Soare), Proc. Amer. Math. Soc. A minimal pair of P classes (with Robert I. Soare), J. Symbolic Logic P classes and degrees of theories (with Robert I. Soare), Trans. Amer. Math. Soc. Degrees of members of P classes (with Robert I. Soare), Pacific J. Math. Ramsey's theorem and recursion theory, J. Symbolic Logic A reducibility arising from the Boone groups, Mathematica Scandinavica Upward closure of bi-immune degrees, Z. Math. Logik Grundlagen Math. Degrees in which the recursive sets are uniformly recursive, Canad. J. Math.

19. Lumpy Pea Coat: Recursion Theory My recursion theory was lacking so I finally cracked open Cutland s computability (that I bought a long time ago and had sitting around the house). http://nortexoid.blogspot.com/2007/06/recursion-theory.html

Lumpy Pea Coat Logic and Mannequins Monday, June 11, 2007 Recursion theory My recursion theory was lacking so I finally cracked open Cutland's "Computability" (that I bought a long time ago and had sitting around the house). It's alright. The exercises are too easy (and a number of them too similar to others) and some of the proofs are sort of lame, not to mention nonconstructive. Just kidding about the nonconstructive part. I'm sure the Rogers text is much better, but these target different audiences (in terms of mathematical sophistication) which I hadn't realized when I picked this up. Anyway, the s-m-n theorem and the Kleene normal form theorem are dope. So is the stuff on reducibility (of decision problems) and degrees of unsolvability. I wish he would've included at least a section on the arithmetical hierarchy. Thankfully it's in Mendelson, which I have. Ha, some Asian guy just walked into the tea house I'm in and the server started talking Mandarin to him, but he's actually North American, so when he started speaking English she didn't know what the hell he said because she was expecting Chinese. She responds "whu!!". I bet some of these American/Canadian-born Asians have it hard in some parts of Asia, like Korea. Ok, nevermindyou had to be here, and be me. I can't wait to be doing logic and philosophy full-time again. Teaching ESL sucks!!! Well, the money is better than anything I could've been doing back home on short notice (since I'm leaving in Sept.), but six days a week is killing me. However, I'm teaching the world a variety of semantic paradoxes one class at a time. (They just look strangely at meno joke.) And everybody thinks that the contradictory of "Everything is P" is "Nothing is P", unless I show them that both can be false. They baffle for a minute, think some more, nothing happens, then...burp.

20. 03: Mathematical Logic And Foundations Notable among postwar developments is Robinson s application of model theory to recursion theory is closely related to questions of computability and http://www.math.niu.edu/~rusin/known-math/index/03-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 03: Mathematical logic and foundations Introduction Mathematical Logic is the study of the processes used in mathematical deduction. The subject has origins in philosophy, and indeed it is only by nonmathematical argument that one can show the usual rules for inference and deduction (law of excluded middle; cut rule; etc.) are valid. It is also a legacy from philosophy that we can distinguish semantic reasoning ("what is true?") from syntactic reasoning ("what can be shown?"). The first leads to Model Theory, the second, to Proof Theory. Students encounter elementary (sentential) logic early in their mathematical training. This includes techniques using truth tables, symbolic logic with only "and", "or", and "not" in the language, and various equivalences among methods of proof (e.g. proof by contradiction is a proof of the contrapositive). This material includes somewhat deeper results such as the existence of disjunctive normal forms for statements. Also fairly straightforward is elementary first-order logic, which adds quantifiers ("for all" and "there exists") to the language. The corresponding normal form is prenex normal form. In second-order logic, the quantifiers are allowed to apply to relations and functions to subsets as well as elements of a set. (For example, the well-ordering axiom of the integers is a second-order statement). So how can we characterize the set of theorems for the theory? The theorems are defined in a purely procedural way, yet they should be related to those statements which are (semantically) "true", that is, statements which are valid in every model of those axioms. With a suitable (and reasonably natural) set of rules of inference, the two notions coincide for any theory in first-order logic: the Soundness Theorem assures that what is provable is true, and the Completeness Theorem assures that what is true is provable. It follows that the set of true first-order statements is effectively enumerable, and decidable: one can deduce in a finite number of steps whether or not such a statement follows from the axioms. So, for example, one could make a countable list of all statements which are true for all groups.

21. Intute: Science, Engineering And Technology - Search Results It shows that when attempting to generalise recursion theory to admissible . They give a comprehensive study of Turing machines, computability theory and http://www.intute.ac.uk/sciences/cgi-bin/search.pl?term1=recursion theory&limit=

22. Logic In Leeds - Postgraduate Opportunities In computability theory, there is a Special Interest Group in Logic and Computation, and relative computability (previously called recursion theory ). http://www.maths.leeds.ac.uk/pure/logic/postgrad.html

People Research Seminars Postgrad opportunities Pure Department School of Mathematics University of Leeds Some outside links Graduate courses Homepage Postgraduate Studies Contents Introduction Current Research in the Mathematical Logic Group Funding International Students ... Enquiries Please also see the School of Maths Postgraduate Brochure , which has far more general information, and puts logic in the context of the other research groups. INTRODUCTION The Department of Pure Mathematics forms part of the School of Mathematics, the other departments being those of Applied Mathematical Studies and Statistics. The department has 20 academic staff, as well as a number of postdoctoral research fellows and research assistants. The Department was rated 5 in both of the last two Research Assessment Exercises. There are usually about 30 research students. As well as the weekly seminars which are mentioned below, there is a less specialised departmental Colloquium which meets once or twice a term. There is also a graduate lecture course each year in each of Mathematical Logic, Algebra, Analysis and Differential Geometry. The aim of the Department of Pure Mathematics at Leeds for many years has been to maintain and develop research groups of international standing in four of the most vital and central areas of mathematics: mathematical logic, algebra, analysis and differential geometry. In each of these subjects there is plenty of lively research activity at Leeds. The department is one of the largest and most active centres for pure mathematics research in the UK, and is an ideal place in which to obtain postgraduate training.

23. Book Recursion Theory (lecture Notes In Logic), Applied Maths For It, Lavoisier of topics to elucidate the concepts of computability and recursion. the of advanced monographs and the current literature on computability theory. http://www.lavoisier.fr/notice/gb094066.html

Search on All Book CD-Rom eBook Software The french leading professional bookseller Description Approximate price Recursion theory (Lecture notes in logic) Author(s) : SHOENFIELD Publication date : 04-2001 Language : ENGLISH Status : In Print (Delivery time : 15 days) Description In this book, the author introduces a broad range of topics to elucidate the concepts of computability and recursion. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on computability theory. It is intended for any reader with some degree of mathematical maturity. Summary Computability. Functions and relations. The basic machine. Macros. Closure properties. Definitions of recursive functions. Codes, indices. Church's thesis. Word problems. Undecidable theories. Relative recursion. The arithmetical hierarchy. Recursively enumerable relations. Degrees. Evaluation of degrees. Large RE sets. Functions of reals. The analytical hierarchy. The projective hierarchy. Subject areas covered: Mathematics and physics Applied maths and statistics Applied maths for it New search Your basket Information New titles BiblioAlerts E-books Customer services Open an account Ordering non-listed items Order tracking Help Lavoisier.fr

24. MPLA :: Graduate Program In Logic, Algorithms And Computation F. Afrati V. Vassalos; 11. recursion theory Y. Moschovakis; 15. Proof theory G. Koletsos G. Stavrinos; 98 . Category theory and Applications http://mpla.math.uoa.gr/courses/full/

mpla.math.uoa.gr Graduate Program in Logic, Algorithms and Computation. Home About Teaching faculty Administration ... Old website Courses Full courses archive By Semester C. Dimitracopoulos Y. Moschovakis http://www.math.uoa.gr/~ymos/l2 E. Koutsoupias http://cgi.di.uoa.gr/~elias/index.cgi/Classes/Year%2020067/Algorithms%2006f D. Richerby http://davidr.phlegethon.org/work/teaching/fmt/ V. Zissimopoulos http://www.di.uoa.gr/~vassilis Y. Moschovakis http://www.math.uoa.gr/~ymos/l02a I. Emiris http://www.di.uoa.gr/~erga/YpolGewmMet.html http://eclass.di.uoa.gr/D231/ N. Papaspyrou http://courses.softlab.ece.ntua.gr/typesys/ http://www.corelab.ntua.gr/courses/cryptograd/ D. Thilikos http://eclass.di.uoa.gr Ì06Â. Ergodic Ramsey Theory V. Farmaki http://www.math.ntua.gr/logic/categories/ S. Kolliopoulos Ì6. Set Theory C. Dimitracopoulos M. Koubarakis E. Raptis F. Afrati E. Kranakis E. Zachos E. Koutsoupias A. Pagourtzis P. Rondogiannis I. Emiris Complexity E. Zachos D. Thilikos D. Richerby top C. Dimitracopoulos Y. Moschovakis E. Koutsoupias Ì11. Recursion Theory Y. Moschovakis

25. Mathematics And Computation » First Steps In Synthetic Computability Theory (Fi computability theory, which investigates computable functions and computable Since I’m studying recursion theory I’m probably biased toward finding the http://math.andrej.com/2005/09/18/first-steps-in-synthetic-computability-theory-

@import url( http://math.andrej.com/wp-content/themes/andrej/style.css ); Mathematics and Computation September 18, 2005 First Steps in Synthetic Computability Theory (Fischbachau) Filed under: Synthetic computability Talks At the EST training workshop in Fischbachau, Germany, I gave two lectures on syntehtic computability theory. This version of the talk contains material on recursive analysis which is not found in the MFPS XXI version of a similar talk. Abstract: topology. Download slides: est.pdf 6 Comments do for a start. Comment by Andrej Bauer Your second question, whether a similar theory may be developed using classical logic, is somewhat misguided. If we want to have a synthetic approach to computability based on the Axiom of Enumerability, then it follows that logic is non-classical (see theorem in the notes which states that the Axiom of Enumerability implies that the Law of Excluded Middle is false). I cannot choose turnes out to be that mathematicians inside the effective topos happen to believe in the Axiom of Enumerability and happen to disbelieve the Law of Excluded Middle, and that things they say about sets mean to us something about computability. Comment by Andrej Bauer do constructive mathematics, without explaining much how to do it. In fact, this may be the best approach: just jump into the constructivist swimming pool and hope there is water in it.

26. Recursion Theory F2003 recursion theory is the study of computability properties of objects like functions and sets of natural numbers, sets of reals etc. http://www.it-c.dk/people/volodya/RTF2003.html

Recursion Theory, Spring 2003 Seminar / reading group / project / PhD course The exam (for the 12-week project, not the PhD course) takes place on Tuesday, June 24 in room starting at . Our internal censor is Lars Birkedal Literature. J. R. Shoenfield. Recursion Theory. Springer-Verlag 1993 (reprinted by A K Peters 2000, ISBN 1-56881-149-7). Episode 1, February 6, 2003. Sections 1 to 4 presented. Homework Exercises (corrected February 10) available for download. Nina's solution to Exercise 6 is now written up. Episode 2, February 13, 2003. We have discussed sections 5 through 7. The discussion unearthed an interesting question about whether there is a single `function algebra term' describing definition by cases for partial (recursive) functions. This question became Exercise 6 in Homework Exercises (corrected February 20). Episode 3, February 20, 2003. We have discussed homework exercises, as well as sections 8 and 9 from the textbook. We focused our attention on the fundamental results of Recursion Theory: the Normal Form, Enumeration, Parametre, and Recursion theorems, as reinforced by Homework Exercises . We have also agreed to accept Church's Thesis as a working hypothesis, at least unless and untill proven wrong.

27. Bibliographic Database For Computability Theory - Extensive Bibliography On Comp Introduction to Logic and recursion theory (Popularity ) Notes from the class taught by Prof. Sacks in the Spring of 1998. computability Logic http://www.sciencecentral.com/site/495421

Sunday, 23 December, 2007 Home Submit Science Site Add to Favorite Contact search for Directories Aeronautics and Aerospace Agriculture Anomalies and Alternative Science Astronomy ... Technology Category: Science Math Logic and Foundations Computability ... REPORT BROKEN LINK Bibliographic Database for Computability Theory Popularity: Details document.write(''); Extensive bibliography on computability and recursion theory, maintained by Peter Cholak. URL Title Description Category: Related sites ECCC - Electronic Colloquium on Computational Complexity (Popularity: ): The Electronic Colloquium on Computational Complexity is a new forum for the rapid and widespread ... Computability Theory (Popularity: ): Directory of researchers working in computability theory, and list of open problems. Computability and Complexity (Popularity: ): An online course on complexity. Problem Solving Environments Home Page (Popularity: ): This site contains information about Problem Solving Environments (PSEs), research, publications, and information on topics ... Hypercomputation Research Network (Popularity: ): The study of computation beyond that defined by the Turing machine, also known as super-Turing, ...

28. Books Classical recursion theory Elsevier, Reprint edition, 1992; Joseph R. Shoenfield computability and Complexity From a Programming Perspective http://www.lab2.kuis.kyoto-u.ac.jp/~tamak/books.html

Suguru Tamaki Useful Books for Theory of Computation Computability, Complexity, Logic, Programming M. R. Garey and D. S. Johnson Computers and Intractability: A Guide to the Theory of NP-Completeness W. H. Freeman, 1979 Christos H. Papadimitriou Computational Complexity Addison Wesley, 1st edition, 1993 Michael Sipser Introduction to the Theory of Computation Course Technology, 2nd edition, 2005 Heribert Vollmer Introduction to Circuit Complexity: A Uniform Approach Springer, 1st edition, 1999 Ingo Wegener The Complexity of Boolean Functions John Wiley and Sons, 1991 Ingo Wegener Branching Programs and Binary Decision Diagrams Society for Industrial and Applied Mathematics, 1987 Eyal Kushilevitz and Noam Nisan Communication Complexity Cambridge University Press, Reissue edition, 2006 Peter Burgisser, Michael Clausen, Mohammad A. Shokrollahi Algebraic Complexity Theory Springer, 1st edition, 1997 Michael J. Kearns and Umesh V. Vazirani An Introduction to Computational Learning Theory The MIT Press, 1994

29. [ecoop-info] CiE 2008 - 1st Call For Papers recursion theory and Applications Algorithmic game theory Quantum algorithms and complexity Biology and computation CiE 2008 conference topics include, http://www.aito.org/pipermail/ecoop-info/2007-September/001746.html

[ecoop-info] CiE 2008 - 1st Call for Papers Arnold Beckmann A.Beckmann at swansea.ac.uk Sat Sep 8 11:43:50 CEST 2007 Previous message: [ecoop-info] FINAL CFP: Internet of Things 2008 (Sep. 15 Deadline) Next message: Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] [Apologies for multiple copies] ****************************************************************** FIRST ANNOUNCEMENT AND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ Previous message: [ecoop-info] FINAL CFP: Internet of Things 2008 (Sep. 15 Deadline) Next message: Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the ecoop-info mailing list

30. CEEL - Summer School - The introduction of computability or recursion theoretic - assumptions in methods and concepts of recursion theory diagonalization, reduction to http://black.economia.unitn.it/summer_school/first/index.html

CEEL Summer school First summer school First Trento Summer School Last update: document.write(document.lastModified) CEEL program in Adaptive Economic Dynamics 25 September - 6 October 2000 First Trento Summer School Intensive course in Computable Economics Program Director : Axel Leijonhufvud Director of the School : K. Vela Velupillai Guest Lecturers The course consists of 3 hours of formal lectures per day for two weeks, supplemented by tutorials and laboratory instructions in the use of SWARM and Mathematica for the computable modelling of economic processes, agents and institutions. This is the first of a series of intensive courses to be offered by the Computable and Experimental Economics Laboratory (CEEL). Five future courses are planned in: Experimental Economics (2001) - Lecturer: Professor Dan Friedman, University of California at Santa Cruz. Adaptive Economic Processes (2002) - Lecturer: Professor Peter Howitt, Brown University. Evolutionary Economic Dynamics (2003).

31. Conference On Logic, Computability And Randomness The Medvedev lattice is a structure from computability theory with ties to with nrandomness in the both recursion theory and set theory aspects. http://www.dc.uba.ar/people/logic2007/

Conference on Logic, Computability and Randomness January 10-13, 2007 Buenos Aires, Argentina program committee submission local organizers plenary speakers ... conference address The theme of the conference will be algorithmic randomness and related topics in logic, computability and complexity. The program will consist of invited talks contributed talks 3 introductory courses. NEW! Check here The booklet with the abstracts of invited and contributed talks is available here See the poster of the conference in jpg or ... YPF Foundation , located in the biggest park in Buenos Aires "los bosques de Palermo" (very near the University campus, Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires The meeting is sponsored by the Association for Symbolic Logic There is no registration fee. Student members of the ASL can apply for travel grants (the approval process takes a few weeks). The spirit of the Conference will be the same as earlier meeting in Córdoba, 2004. The booklet with the abstracts of invited and contributed talks of the earlier meeting is available here If you wish to attend to the conference (and you are not giving a talk) please let us know in advance.

32. Discrete Math II Last semester concentrated on functions, number theory, recurrence equations, recursion, combinatorics, and their Applications. http://www.stonehill.edu/compsci/Discrete-Math-II/homepage.htm

CS 202 - Discrete Mathematics for Computer Scientists II Shai Simonson 306 Stanger (508) 565-1008 Email: shai@stonehill.edu Homepage: http://www.stonehill.edu/compsci/shai.htm Lectures: TTh 1:00 - 2:15, 001 Stanger Texts: Discrete Mathematics and its Applications, Rosen, McGraw Hill. Pettofrezzo, Anthony J. Matrices and Transformations. New York: Dover, 1978. Exams: There will be one midterm (25%) and one final examination (35%). Teaching Assistant: TBA Assignments: Homeworks will be worth 40% of your grade. You may do these with a partner, and one grade will be given to both people in the group. Goals: To understand the mathematics that underlies computer science, and to appreciate where it is used. Last semester concentrated on functions, number theory, recurrence equations, recursion, combinatorics, and their applications. This semester concentrates on sets, graphs, Boolean algebra, linear algebra, and their applications. Special Dates: I will not be here on Tuesday, April 18, and Thursday, April 20 due to Passover. The lecture on April 18 is cancelled. The April 20 date will be used for homework review, and/or finishing CLO project. Description: Useful Links Mathworld Cut-the-Knot Google's Ranking Method History of Set Theory ... The Paper Assignments If you haven't done it yet, then read

33. Upcoming Conferences | Doctoral Program In Computer Science computability in Europe, Logic and theory of Algorithms (CiE08) science Games Generalized recursion theory History of computation Hybrid systems Higher http://146.96.245.153/news/conferences

@import "/files/css/2597047487d9c0e0d4a278c2d2595805.css"; @import "/themes/rose/print.css"; Login Search Links Location ... Links Upcoming Conferences 08-03-28 VII Jornadas de Ingenier­a Telem¡tica (2008) Thu, 12/20/2007 - 14:22 VII Jornadas de Ingenier­a Telem¡tica (Jitel2008-08) Date:Sep 16 08 to Sep 18 08 Deadline:Mar 28 08 Location:Alcal¡ de Henares, Spain Url: http://www.jitel.org/ Categories: Upcoming Conferences 08-01-25 Optimisation in Multi-Agent Systems (2008) Thu, 12/20/2007 - 11:27 Optimisation in Multi-Agent Systems (OptMAS-08) Date:May 12 08 Deadline:Jan 25 08 Location:Estoril, Portugal Url: http://www.optmas08.org/ Categories: Upcoming Conferences 08-01-25 Workshop on Agent-based Complex Automated Negotiation (2008) Thu, 12/20/2007 - 11:22 Workshop on Agent-based Complex Automated Negotiation (ACAN-08) Date:May 12 08 Deadline:Jan 25 08 Location:Estoril, Portugal Url: http://www-itolab.mta.nitech.ac.jp/ACAN2008/ Categories: Upcoming Conferences 08-03-24 Twelfth International Workshop on Cooperative Information Agents (2008) Thu, 12/20/2007 - 11:12 Twelfth International Workshop on Cooperative Information Agents (CIA-08) Date:Sep 10 08 to Sep 12 08 Deadline:Mar 24 08 Location:Prague, Czech Republic Url:

34. Recursion Theory - Wikipedia, The Free Encyclopedia The main form of computability studied in recursion theory was introduced by .. On computable numbers, with an application to the Entscheindungsproblem. http://en.wikipedia.org/wiki/Recursion_theory

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Recursion theory From Wikipedia, the free encyclopedia Jump to: navigation search For the branch of computer science called computability theory, see Computability theory (computer science) Recursion theory , also called computability theory , is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees . The field has grown to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory The basic questions addressed by recursion theory are "What does it mean for a function from the natural numbers to themselves to be computable?" and "Can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched. Recursion theorists in mathematical logic often study the theory of relative computability, reducibility notions and degree structures described in this article. This contrasts with the theory of subrecursive hierarchies formal methods and formal languages that is common in the study of computability theory in computer science . There is considerable overlap in knowledge and methods between these two research communities, however, and no firm line can be drawn between them.

35. Computability Theory Directory of researchers working in computability theory, and list of open problems. http://www.nd.edu/~cholak/computability/computability.html

Computability Theory Bibliographic Database for Computability Theory Open Questions in Recursion Theory Other Useful Sites: Association for Symbolic Logic People who work (or have worked) in Computability Theory: Klaus Ambos-Spies George Barmpalias Valeriy Bulitko Sam Buss ... Sy Friedman Edward R. Griffor Valentina Harizanov Leo Harrington Charles Harris Denis R. Hirschfeldt ... Bjørn Kjos-Hanssen Antonin Kucera Steve Homer Carl Jockusch Alistair Lachlan Geoffrey LaForte ... Iraj Kalantari Jan Kraijeck Matrin Kummer David Marker Yiannis Moschovakis Anil Nerode Andre Nies ... Stan Wainer Dongping Yang Mike Yates People whose work had great impact on the field: Charles Babbage Alonzo Church Robin Gandy Reuben Goodstein ... Computability Theory E-mailing List Research Announcements Recursive Function Theory Newsletter Meetings (see the Association for Symbolic Logic for ASL meetings) Research Grants Computability in Europe (CiE). Graduate School in Computability Theory The University of Connecticut Math Department Univeristy of Notre Dame Job Announcements As with most web pages, this page is a continuously evolving resource. It will only develop into a useful resource for computability theorists if they help by adding information related to computability theory to the web and this page. Therefore computability theorists are encouraged to add information and links to this page. There are two ways of achieving this. The preferred method is to add the information to the web yourself and

36. Classical Recursion Theory, Volume II - Elsevier Volume II of Classical recursion theory describes the universe from a local (bottomup which constitutes the core of recursion or computability theory. http://www.elsevier.com/wps/product/cws_home/620333

Home Site map Elsevier websites Alerts ... Classical Recursion Theory, Volume II Book information Product description Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view CLASSICAL RECURSION THEORY, VOLUME II To order this title, and for more information, click here By P. Odifreddi , University of Turin, Italy Included in series Studies in Logic and the Foundations of Mathematics, 143 Description Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus.

37. Computer Science And Recursion Theory We discuss how recursion theory supplied computer science with specific mathematical . 52 Turing, A.M. On computable numbers with an application to the http://portal.acm.org/citation.cfm?id=804061&dl=ACM&coll=portal

38. Recursion Theory recursion theory. The field of recursive analysis develops natural number computation into a framework appropriate for the real numbers. http://mulhauser.net/research/tutorials/computability/recursion.html

You have reached part of the Mulhauser Consulting legacy site. Please note that the legacy pages of the Mulhauser Consulting site have not been actively maintained since 2003. Please click to visit the current home page of Mulhauser Consulting, Ltd. Research Front Page Research Details Research Summary Mind Out of Matter Resources Bibliographies Draft Papers Robots Workshop Related Destinations BTexact Technologies Santa Fe Institute Greg Chaitin's Pages ENTROPY Journal ... Advertising Policy Sections Available: Computability Theory Classical/Halting Recursive Analysis Super-Turing ... Counselling Scientific Research Web mulhauser.net This article outlines a standard definition of computability for the real numbers. Introduction Recursion Theory An Interesting Connection With Analogue Computation Introduction another short paper on the topic . The basic problem of incompleteness has been extended to its most general form by Greg Chaitin, and the theory of Turing computation over the naturals can be usefully developed to include algebra and fields ( Rabin 1960 ). But the fact that real physical systems are normally described by functions which take on real values motivates the extension of Turing computation to cover the real numbers

39. LC 2002 Abstracts Computable subsets of Banach spaces and their application in computable functional analysis .. Proof theory and recursion theory of the mucalculus http://www.math.uni-muenster.de/LC2002/abstracts.html

40. IngentaConnect Recursion Theory On The Reals And Continuous-time Computation recursion theory on the reals and continuoustime computation. Author Moore C.1. Source Theoretical Computer Science, Volume 162, Number 1, 5 August 1996 http://www.ingentaconnect.com/content/els/03043975/1996/00000162/00000001/art002

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Recursion theory on the reals and continuous-time computation Author: Moore C. Source: Theoretical Computer Science , Volume 162, Number 1, 5 August 1996 , pp. 23-44(22) Publisher: Elsevier view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Language: English Document Type: Research article DOI: Affiliations: Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA

41. Computation, Automata, Languages AI/0511073 Cristopher Moore, recursion theory on the Reals and ContinuousTime Computation, Theoretical Computer Science, 162 (1999) 2344 http://www.cscs.umich.edu/~crshalizi/notebooks/computation.html

Notebooks Computation, Automata, Languages 07 Oct 2007 22:17 Computers aren't made of matter. - Greg Egan, Permutation City Ideal, theoretical computers are rather mathematical objects: they are, equivalently, algorithms, or effective procedures, or abstract automata, or functions which can be specified recursively, or formal languages. Things to learn more about: Classifications of machines and languages (beyond the classical, four-level Chomsky hierarchy). Hierarchies of computational power. Abstract-algebraic treatment of automata. Effects of making automata stochastic. Techniques for proving equivalence of automata; of minimizing automata. Bisimulation. Techniques for inferring automata or grammars from their languages, especially when generation is stochastic . Non-finite-state transducers. Stochastic context-free grammars and their connections with branching processes . "Logics of time and computation". Analog computation. What forms are structurally stable? Other forms of unconventional computation. DNA computation doesn't interest me very much, because that's just another kind of hardware, and slow, big and noisy at that. But quantum computation is very interesting, because it can do something new. So, possibly, is computation in dynamical systems. Complexity classes - in space (memory), time, other resources? Analog equivalents. "Phase transitions" between complexity classes, and the analogy to physical phase transitions.

42. Recursion Theory - Wiki Browser By Chainofthoughts.com Linear logic Firstorder logic Reduction (recursion theory) Second-order arithmetic Reasoning Natural number List of set theory topics computability logic http://wiki.chainofthoughts.com/dt/en/Recursion theory

Recursion theory links Linear logic First-order logic Reduction (recursion theory) ... merkl

43. Algorithmic Information Theory 3rd Annual Conference on theory and Applications of Models of Computation (TAMC), LNCS3959, 408420, 2006. R. Cilibrasi and P.M.B. Vitanyi, Clustering by http://www.hutter1.net/kolmo.htm

This page has been moved to http://www.hutter1.net/ait.htm

44. Applications Of Algorithmic Information Theory - Scholarpedia recursion theory to analyse notions of randomness, this line of research is .. While this metric is not computable, it has an abundance of Applications. http://www.scholarpedia.org/article/Applications_of_Algorithmic_Information_Theo

Applications of Algorithmic Information Theory From Scholarpedia Ming Li and Paul M.B. Vitanyi (2007), Scholarpedia, 2(5):2658. revision #12453 [ cite this article Curator: Ming Li, University of Waterloo Curator: Paul M.B. Vitanyi, CWI , and Computer science, University of Amsterdam Algorithmic Information Theory , more frequently called Kolmogorov complexity , has a wide range of applications, many of them described in detail by Li and Vitanyi (1997/2007) . The range of applications is so vast that every such selection cannot be comprehensive or even cover all important items. The applications can use the property that: most strings are effectively incompressible, or some strings can be effectively compressed, or some strings can be effectively compressed but take a lot of effort to do so, or different strings can be effectively compressed in various degrees, singly, jointly, or conditionally on one another, and that approximating the Kolmogorov complexity with real-world compressors still gives acceptable, or even very good, results. Contents Application of Incompressibility List of selected application areas A simple example from number theory Example: Goedel's incompleteness result ... edit Application of Incompressibility A new mathematical proof technique was developed, now known as the

45. Computing With Reals - Some History recursion theory provides a basis for an understanding of computability separated from too great an exposure to philosophy. http://www.rbjones.com/rbjpub/cs/cs006.htm

Computing with Reals Some History Reals - how they might have developed Thumbnail History of Reals Constructive Mathematics Alan Turing (1936) ... Other Recent Work I have myself been interested in this area for at least 20 years, (or, since the publication of Minsky's book, depending on what you count as interest). It has never got high enough on my priority list for more than the odd tinker. Recently my interest was revived because I was thinking about theorem provers capable of doing automatically computations in real analysis, and for this purpose the ability to do exact computations with reals is essential (IMO). The following is my best shot at an outline of the history of the subject. I have no doubt whatever that the story is incomplete, and its probably wrong too. If you know better, spare me a few minutes to help brush up or fill in the picture. Constructive Mathematics The story surely must start here. Its not easy to say where constructive mathematics starts, historically, since some say that maths always was constructive until non-constructive techniques appeared in the 19th century. However, the emergence of intuitionism, the first explicitly constructive doctrine, as a distinct thread in mathematical philosophy is a phenomenon of the early twentieth century. I believe that intuitionism was the first brand of constructivism to emerge, and has been followed by many others. Constructive mathematics is distinguished by a particular concern for the computational content of mathematics, and often by a rejection of classical mathematics and classical logics. Classical mathematics is founded in Cantor's set theory, which builds up to (and beyond) the complex analysis widely exploited in science and engineering. Some of the criticisms, levelled by intuitionists and other constructivists againsts classical mathematics at a time long before the invention of digital computers (or even Turing machines), are not so very far from the feelings which a scientifically oriented software engineer might feel about the use in science of number systems which simply aren't implementable computationally.

46. Recursion Theory » Wikirage: What's Hot Now On Wikipedia recursion theory. « Summary from Wikipedia 1635, 24 October 2007 137.222.98.63 (Talk) (40215 bytes) ( Generalizations of Turing computability) http://www.wikirage.com/wiki/Recursion_theory/

This site lists the pages in Wikipedia which are receiving the most edits per unique editor over various periods of time. 1-25 for Akatsuki (Naruto) I Am Legend (film) Nancy Reagan The Amazing Race 12 ... Jiraiya (Naruto) Summary from Wikipedia Recent Edits 12:32, 21 December 2007 Jdrewitt Talk contribs (40,252 bytes) Undid revision 179379870 by talk 12:32, 21 December 2007 Talk (40,253 bytes) Frequency computation 12:31, 21 December 2007 Talk (40,252 bytes) Frequency computation 12:30, 21 December 2007 Talk (40,253 bytes) Inductive inference 08:50, 18 December 2007 Talk (40,255 bytes) Research papers and collections - +ja) 20:59, 28 November 2007 JMK Talk contribs m (40,235 bytes) 16:41, 28 October 2007 Talk (40,237 bytes) (interwiki) 16:35, 24 October 2007 Talk (40,215 bytes) Generalizations of Turing computability var AdBrite_Title_Color = '0000FF'; var AdBrite_Text_Color = '000000'; var AdBrite_Background_Color = 'FFFFFF'; var AdBrite_Border_Color = 'FFFFFF'; Historical Top Edits Rankings 1 Hours 3 Hours 6 Hours 12 Hours 24 Hours 48 Hours 72 Hours 168 Hours 336 Hours 672 Hours Number of Unique Editors per 12 hour segments over last 28 days Feedback and/or Questions Tell me about your wiki tools and charts.

47. Selected Talks (Lars Kristiansen) The Tradeoff Theorem and Fragments of Gödel s T. TAMC2006 theory and Applications of Models of Computation, Beijing China 15 May - 20 May, http://www.iu.hio.no/~larskri/foredrag.html

Selected talks Beregnbarhet, kompleksitet og typeteori (Computability, complexity and type theory). Felleskollokviet (Mathematics Colloquium), Department of Mathematics, University of Oslo, March 30, 2007. PCC '07 - International Workshop on Proof, Computation, Complexity. Swansea, Wales, April 13-14, 2007. Neil Jones: The early years. Talk given at A TRIBUTE WORKSHOP AND FESTIVAL TO HONOR Professor Dr. Neil D. Jones , Copenhagen, 25-26 August, 2007 Complexity-Theoretic Hierarchies Copenhagen Programming Language Seminar, March 30, 2006, DIKU. Invited talk. TAMC2006: Theory and Applications of Models of Computation, Beijing China 15 May - 20 May, 2006 (Joint work with Paul Voda.) Complexity-Theoretic Hierarchies. CiE 2006 - Computability in Europe 2006: Logical Approaches to Computational Barriers, University of Wales Swansea 30 June - 5 July, 2006. PCC '06 - 6th International Workshop on Proof, Computation, Complexity. Ilmenau, Germany, July 25-26, 2006. "Workshop on Proof Theory and Rewriting", Obergurgl University Center, September 5-9 2006, Austria. Static Complexity Ananlysis of Programs.

48. Study And Teaching The central application area is the analysis and synthesis of reactive systems . recursion theory is the theory of the computable . http://www.informatik.rwth-aachen.de/Studierende/Vertiefung/ls7_eng.php

Hauptnavigation Homepage News Workgroups Servicegroups ... back to specialisation-overview Inhalt der Seite Theoretische Informatik: Automaten, Logik und Verifikation The research topics and projects of the Chair for Computer Science 7 are described on the chair's webpage under " Research/Projects " and " Diploma Theses ". The area of specialisation for the diploma examination in computer science is "Automata, Logic and Verification". Prof. Dr. Wolfgang Thomas is the examiner. The chair offers courses from the list below on a regular basis. There may be changes due to the introduction of the Master program in computer science (presumably winter term 2008/2009). This course first offers an introduction to the theory of automata on infinite words. The central application area is the analysis and synthesis of "reactive systems". These are systems such as controllers and communication protocols, in which two features are essential: Usually they do not terminate, and they are in continuous interaction with their environment. In the first part of the course we concentrate on the specification of non-terminating behaviour. For this purpose one uses finite automata which accept infinite words. Many results of the theory of automata on finite words can be transferred to the case of infinite words, but more complex constructions are necessary. We also present the connection between automata and logical systems and introduce the method of "model-checking", the algorithmic verification of state-based systems.

49. Longo Symposium 1540 – 1700, Session 7 Analysis, Physics, and recursion theory Abbas Edalat Recursively measurable sets and computable measurable sets Thierry Paul http://www.pps.jussieu.fr/~gc/other/rdp/talks.html

28-29 June 2007 From Type Theory to Morphologic Complexity: A Colloquium in Honor of Giuseppe Longo In conjunction with RDP 2007 Paris, Conservatoire National des Arts et M©tiers , Amphitheaters 3 and A. This colloquium was organised to celebrate the 60th birthday of Giuseppe Longo . Some photos of the meeting can be found here The main research area Giuseppe Longo has been interested in concerns syntactic and semantic properties of the "logical base" of functional languages: Combinatory Logic, Lambda-calculus and their extensions. However, he always investigated these topics in its broadest setting which relates them to Recursion Theory, Proof Theory and Category Theory. In this perspective, Longo worked at some aspects of Recursion Theory, Higher Type Recursion Theory, Domain Theory and Category Theory as part of a unified mathematical framework for the theory and the design of functional languages. In a sense, Longo has always been mostly interested in the "interconnecting results" or "bridges" and applications among different areas and to language design. He also worked at the applications of functional approaches to Object-Oriented programming. He is currently extending his interdisciplinary interests to Philosophy of Mathematics and Cognitive Sciences. A recent interdisciplinary project on Geometry and Cognition (started with the corresponding grant: "G©om©trie et Cognition", 1999 - 2002 with J. Petitot et B. Teissier), focused on the geometry of physical and biological spaces. The developements of this project lead to a new initiative at DI-ENS, in 2002, the setting up of the research team "Complexit© et information morphologiques" (CIM), centered on foundational problems in the interface between Mathematics, Physics and Biology.

50. Dr Benedikt Loewe: Recursion Theory (1st Semester 2003/2004) UvA Logo. recursion theory 2003/2004; 1st Semester Institute for Logic, Language Computation Universiteit van Amsterdam http://staff.science.uva.nl/~bloewe/2003-I-RT.html

Recursion Theory 2003/2004; 1st Semester Universiteit van Amsterdam Instructor: Dr Benedikt Löwe Vakcode: Time: Thursday 3-5 Place: P.015A First Lecture: September 11th, 2003 (Note that there will be no lecture on September 4th due to the traditional Introductory Boat Trip of the Master of Logic program. Also, there will be no lecture on October 23rd.) Course language: English Intended Audience: MoL students, Mathematics students in their fourth year Prerequisites: This course assumes basic mathematical skills and some knowledge of basic logic. This course will cover the basic notions of computability: Turing machines, recursivity and computer programs. The Equivalence Theorem will lead to Church's Thesis. Having a formalization of computability allows us now to investigate the boundaries of computation: what problems are not computationally solvable? This question will lead us to Turing's Halting Problem and the Decidability. We discuss several notions of recursion theoretic reducibility, their derived degree structures, and mathematical properties of these structures. We shall mostly follow Part A of the textbook Robert I.

51. Gordon: Comparisons Between Some Generalizations Of Recursion Theory To do any kind of computation or recursion theory one must work within a rich . computable relation on x. The proof is a direct application of (2.6). http://www.numdam.org/numdam-bin/fitem?id=CM_1970__22_3_333_0

52. Recursion Theory, Or Recursive Function Theory (logic) -- Britannica Online Enc recursion theory in turn led to the theory of computable functions,. As a result of the development of recursion theory, it is now possible to prove not http://www.britannica.com/eb/topic-493971/recursion-theory

Already a member? LOGIN Encyclopædia Britannica - the Online Encyclopedia Home Blog Advocacy Board ... Free Trial Britannica Online Content Related to this Topic Shopping Revised, updated, and still unrivaled. 2008 Britannica Ultimate DVD/CD-ROM The world's premier software reference source. Great Books of the Western World The greatest written works in one magnificent collection. Visit Britannica Store recursion theory, or recursive function theory (logic) A selection of articles discussing this topic. metalogic modern logic ...on what cannot be validly deduced from a set of material hypotheses. One attempts to find structures about which the hypotheses are true and yet for which a particular statement is false. Third is recursion theory, which deals with questions involving the decidability of the question of whether or not a sentence is deducible from a set of premises. This study has led to theories of... No results were returned. Please consider rephrasing your query. For additional help, please review Search Tips Search Britannica for recursion theory About Us Legal Notices ... Test Prep Other Britannica sites: Australia France India Korea ... Encyclopedia

53. CiE Talks Felix Costa The New Promise of Analog Computation; Natasha Jonoska Computing by Selfassembly; Giancarlo Mauri Membrane Systems and Their Applications http://www.mat.unisi.it/~sorbi/sito/

Plenary Tutorials Contributed Talks: Contributed 1 Contributed 2 Contributed 3 Contributed 4 ... Contributed 5 Special Sessions: Doing without Turing Machines: Constructivism and Formal Topology Approaches to Computational Learning Real Computation Computability and Mathematical Structure ... Computational Foundations of Physics and Biology Plenary Lessons: Pergiorgio Odifreddi : Introductory Lecture Roger Penrose : The Issue of Non-Computability in Physical Laws Philip Welch :Turing Unbound: Transfinite Computation Anil Nerode Logic and Control Michael Rathjen : Theories and Ordinals in Proof Theory Sophie Laplante : Quantum vs Classical Theories: Simulating Quantum Correlations with Classical Resources Stephen A. Cook : Low Level Reverse Mathematics Anne Condon : Computational challenges in prediction and design of nucleic acid structure Wolfgang Maass Theoretical Aspects of Biological Computation Robert I. Soare : Computability and Incomputability Yuri Ershov :HF-Computability Dana S. Scott Looking to the Future Back to top Tutorials: Pieter W. Adriaans

54. Bounded Queries In Recursion Theory In recursion theory one considers functions which can be computed by an An important measure of the complexity of a computable function is the time http://www.ici.ro/ici/revista/sic2000_4/art15.htm

Bounded Queries in Recursion Theory by William I. Gasarch and Georgia A. Martin Progress in Computer Science and Applied Logic: Vol. 16 ISBN 0-8176-3966-7 In recursion theory one considers functions which can be computed by an algorithm. Computational complexity theory is dedicated to the study of the difficulty of computations based on the notion of a measure of computational complexity in terms of the amount of some resources a program uses in a specific computation. An important measure of the complexity of a computable function is the time needed to compute it. Other resources, such as space , have also been considered. The object of the book is to classify functions which are not calculable from the point of view of their difficulty , in a quantitative way. For this, a new notion of complexity that is quantitative is introduced such that it expresses the level of difficulty of a function (such as the Turing degree). This work is a reflection of the contribution of the authors to the foundation and the development of a new direction of research in computational complexity theory. An oracle Turing machine is defined as a Turing machine together with an extra tape, an extra head to be used for reading that tape, and a mechanism to move the extra head and to overwrite characters on the extra tape. This notion is considered as a model of computation which extends the usual model of Turing machine to the power of asking questions - called