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1. RANDOM SETS IN SUBRECURSIVE HIERARCHIES, Successive modifications of Church s definition of a random sequence are considered in terms of their relative position in the Ritchie hierarchy of Kalmar http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0

2. Random Sets In Subrecursive Hierarchies A general result is derived governing the classification of Church random sequences in subrecursive hierarchies which include the elementary functions, http://portal.acm.org/citation.cfm?id=321541.321551

3. JSTOR Random Sets In Subrecursive Hierarchies. Random sets in subrecursive hierarchies. Journal of the Association for Computing Machinery, vol. 16 (1969), pp. 621630. As in the paper reviewed above, http://links.jstor.org/sici?sici=0022-4812(197506)40:2<249:RSISH>2.0.CO;2-J

4. Review Robert A. DiPaola, Random Sets In Subrecursive Hierarchies Robert A. DiPaola, Random Sets in subrecursive hierarchies. Fulltext Access via JSTOR (no additional login). Go to this article in JSTOR http://projecteuclid.org/handle/euclid.jsl/1183739409

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Review: Robert A. DiPaola, Random Sets in Subrecursive Hierarchies Donald W. Loveland Source: J. Symbolic Logic Volume 40, Issue 2 (1975), 249-250. Reviewed Items: Robert A. DiPaola, Random Sets in Subrecursive Hierarchies. Full-text: Remote access If you are a member of the ASL, log in to Euclid for access. Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR. Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.jsl/1183739409 JSTOR: links.jstor.org back to Table of Contents previous next Journal of Symbolic Logic Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

5. Project: Phase Transitions In Logic And Combinatorics It contains the sharpest threshold for subrecursive hierarchies which can be found in the literature. paper 5 appeared in the JSL. http://cage.ugent.be/~weierman//phase.html

Phase transitions in Logic and Combinatorics Project of Andreas Weiermann If anybody wants to join - students are welcome -, please let me know. I plan to built a group of approximately ten (to start with) collaborateurs. In particular I would like to integrate a mathematical physicist. There seem to be analogues of renormalization and universality in this new branch of logic. Generous support by DFG (projects We 2178-2,We 2178-3, We 2178-4, We 2178-5,We 2178-6) and NWO (project 613.080.000) is hereby acknowledged. Gyesik Lee's 2005 DFG funded dissertation emerged from the project. A first selection of project relevant papers: paper 1, appeared in MDMV 2005. paper 2 appeared in APAL 2005. paper 3 appeared in the Proceedings of the MSJ meeting in Okayama 2005. That contribution is an extended version of the paper 1 in German. paper 4 is accepted for MSCS. It contains the sharpest threshold for subrecursive hierarchies which can be found in the literature. paper 5 appeared in the JSL. It contains the sharp threshold for Kruskal's theorem and epsilon_0. This paper has been crucial for the genesis of the project. paper 6 appeared in the Proceedings of the AMS. It contains the sharp threshold for the Paris Harrington theorem.

6. A Note On Comparison Of Subrecursive Hierarchies. D2R Server A Note on Comparison of subrecursive hierarchies. Resource URI http//dblp.l3s.de/d2r/resource/publications/journals/ipl/Tsichritzis71 http://dblp.l3s.de/d2r/resource/publications/journals/ipl/Tsichritzis71

7. Logic In Leeds - Postgraduate Opportunities (ii) subrecursive hierarchies, measuring and classifying computable objects and their algorithms according to their logical and computational complexity. 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.

8. Libra: Random Sets In Subrecursive Hierarchies Random Sets in subrecursive hierarchies(1969). Order By. Year, Rank. Year = 1997. Resource Bounded Randomness and Computational Complexity(1997) http://libra.msra.cn/papercited.aspx?id=786642

9. Ordinal Complexity Of Recursive Programs And Their Termination Proofs The treatment is based on that given by Dennis Jones and Wainer in their paper ``subrecursive hierarchies via Direct Limits . The idea of a decomposable http://www.lfcs.inf.ed.ac.uk/reports/92/ECS-LFCS-92-196/

People Events Research Home Ordinal Complexity of Recursive Programs and their Termination Proofs Matthew V H Fairtlough Abstract: structured tree-ordinal is defined. We proceed to give a category-theoretic treatment of these tree-classes and of the Slow-Growing Hierarchy G defined over them. The treatment is based on that given by Dennis Jones and Wainer in their paper ``Subrecursive Hierarchies via Direct Limits''. The idea of a decomposable morphism is introduced, allowing us to define G as a functor in its ordinal arguments as well as in its numerical ones. In chapter two new notions of elementary and primitive recursive ordinals are given, in the context of the material developed on tree-ordinals. The aim is to sidestep the collapsing phenomenon (every recursive function is definable by recursion on an elementarily coded well-order of order type w ) which prevents a subrecursive classification using set-theoretic ordinals. The main theorem is a reformulation in terms of tree-ordinals of the result that every elementary number-theoretic function is bounded by some fixed iterate of the exponential function x maps to x The third chapter explores the connection between hierarchies of number- theoretic functions and various developments of the w . There is a section on cut elimination, which shows how proofs in a proof system with one form of cut can be reduced to proofs in a system with a weaker form of cut.

10. Search Result Query title = Random Sets in subrecursive hierarchies. 1, EE Robert A. Di Paola Random Sets in subrecursive hierarchies. http://www.informatik.uni-trier.de/ley/dbbin/dblpquery.cgi?title=Random Sets in

11. OZSL Orgnanizes, In Collaboration With The Heyting Foundation A Title subrecursive hierarchies and Independence Results Abstract We give a short introduction into subrecursive hierarchies. http://www.phil.uu.nl/~ruben/OZSL/schoolweek/

Abstracts OZSL Schoolweek Title: The many faces of provability Speaker: Lev Beklemishev The notion of proof stands out as one of the central concepts in Logic. Notions of proof do not only occur in mathematics - one encounters proof-like concepts in many different fields, such as computer science (software verification), criptography (`interactive proofs'), legal reasoning (`defeasible proof'), etc. We shall examine various aspects of the notion of proof: distinctions between formal and informal proofs, relations between proof and computation, between provability and truth. Thus, the lecture provides a perspective of the main topics of interest for this School-week: provability logic, proof theory and automated proofs. Title: The quest for correctness; a general introduction to computer mathematics Speaker: Henk Barendregt Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This not in spite of, but computer systems for a full integration of defining, computing and

12. Hierarchies And Machine Description Of Small Subrecursive Classes Hierarchy gap results for small subrecursive classes are given in this work for analogs of Grzegorczyk classes for simultaneous (vector) and word bounded http://logic.ru/en/node/328

13. IngentaConnect A Uniform Approach For Characterizing The Provably Total Number-T In this article we show how to extract with the use of the BuchholzCichon-Weiermann approach to subrecursive hierarchies from Rathjen s 1991 ordinal http://www.ingentaconnect.com/content/klu/stud/1999/00000062/00000003/00231230;j

14. 03Dxx 68Q17; 03D20 Recursive functions and relations, subrecursive hierarchies 03D55 hierarchies; 03D60 Computability and recursion theory on ordinals, 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

15. 91SUB.TEX Renamed Msc.new EDITED FOR SCREEN USE 11-28-90 % 11-29 subrecursive hierarchies 03D25 Recursively enumerable sets and degrees 03D30 Other isols 03D55 hierarchies 03D60 Recursion theory on ordinals, http://www.math.uiuc.edu/documenta/AMS-MSC/MSC91

16. Abstracts Of Papers And Notes Abstract A brief introduction to subrecursive hierarchies and related topics, but not intended as a detailed account. The notes deal with such topics as http://www.cs.man.ac.uk/~hsimmons/DOCUMENTS/papersandnotes.html

Abstracts of Papers and Notes These documents are listed in reverse chronological order, that is with the latest at the top and the earliest at the bottom. Each is given a label consisting of a number together with either P (for Paper) or N (for Notes). Some of the Papers have already been published or I intend to submit them for publication. Others I will simply leave here, at least for the time being. Where available, after each abstract there are links to various forms of each of that document. The directory contains all of the available documents, The Ackermann functions are not optimal, but by how much? Abstract : The Ackermann functions are examples of functions that are not primitive recursive but are clearly recursive in some sense. I show that these functions are far from being optimal examples of this phenomenon. 25 pages Paper can be found at Ackermann.pdf Fruitful and helpful ordinal functions Abstract : This is a companion to (03P) `A comparison of two systems or ordinal notations'. In it I set down some of the details that are missing from that paper. Some of the material is extracted from (04P). 19 pages Preliminary version from FruitHelp.dvi.

17. 1991 Mathematics Subject Classification (MSC 1991) 03D20 Recursive functions and relations, subrecursive hierarchies 03D55 hierarchies; 03D60 Recursion theory on ordinals, admissible sets, etc. http://www.zblmath.fiz-karlsruhe.de/MATH/msc/msc91

1991 Mathematics Subject Classification (MSC 1991) 00-XX General Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) General and miscellaneous specific topics General mathematics Mathematics for nonmathematicians (engineering, social sciences, etc.) Problem books Recreational mathematics Bibliographies Dictionaries and other general reference works Formularies Methodology of mathematics, didactics Theory of mathematical modeling General methods of simulation Dimensional analysis Physics (use more specific entries from Sections 70 through 86 when possible) Miscellaneous topics Conference proceedings and collections of papers Collections of abstracts of lectures Collections of articles of general interest Collections of articles of miscellaneous specific content Proceedings of conferences of general interest Proceedings of conferences of miscellaneous specific interest Festschriften Volumes of selected translations Miscellaneous volumes of translations 01-XX General reference works (handbooks, dictionaries, bibliographies, etc.)

18. CiE-CS: Special Sessions Andreas Weiermann (Utrecht) Phase transition results for subrecursive hierarchies and rapidly growing Ramsey functions. Special Session on Real Computation http://www.illc.uva.nl/CiE/index.php?page=6

19. Home Page Of Andreas Weiermann Pi^1_2logic, subrecursive hierarchies, provably recursive functions, which deal with growth rate classifactions of the slow growing hierarchy. http://wwwmath1.uni-muenster.de/u/weiermann/

Old Home Page of Andreas Weiermann Picture of me together with Alan Woods in Oberwolfach during our wonderful RIP stay. Address Prof. Dr. Andreas Weiermann Einsteinstr. 62 e-mail: weierma(at)math(dot)uni(hyphen)muenster.de phone: (X49)251-8333762 phone: (X49)251-8333762 (X49)251-8333790 (secretary of the Institute) (X49)251-8333060 (secretary of the Institute) (X49)251-8333078 (fax) Address in Utrecht: Institut for Wiskunde en Informatica Budapestlaan 6 3548 Utrecht email: weierman(at)math(dot)uu.nl Homepage in Utrecht Scientific awards, grants and projects till 2003 The information on this page is representative till the end of 2003. For recent information please consult my Utrecht homepage. Utrecht is a place which provides a very nice competitive scientific environment for high quality research in logic in general (and proof theory in particular) and mathematics. I am still a Heisenberg fellow of the DFG. The Deutsche Forschungsgemeinschaft has supported my research in addition by sponsoring a two years project for Gye Sik Lee and a two years project for Ingo Lepper. Moreover I am scientist in charge for a Marie Curie fellowship of Georg Moser. Recently the DFG has funded a joint project with Alan Woods about analytic combinatorics and logical limit laws and a joint project with Harvey Friedman and Toshiyasi Arai about the fine structure of independence results. From 1.9.1994-31.3.1995 I was sponsored by a HCM-grant from the European Community. From 1985-88 I was Stipendiat of the Studienstiftung des Deutschen Volkes.

20. Seminars Transfinite subrecursive hierarchies of bounding functions provide a linear scale against which prooftheoretic strength can be measured and compared. http://math.nju.edu.cn/~yuliang/Seminar.html

Logic Seminar at IMS [2] 3:00-5:00pm, 12/Sep/2006:Computable Riesz representation theorems. Speaker: Hong Lu. [3]3:00-5:00pm, 19/Sep/2006:Variable Minimal Characteristics of Approximations. Speaker: Zhenyu Chen. We first introduce the definition of approximation, i.e. a sub-formula with less variables. We present a method to construct the most accurate approximations. Furthermore, we consider the variable minimal approximations with some characteristics, so-called variable minimal equivalence (VME), variable minimal satisfiability (VMS), and variable minimal unsatisfiability (VMU), respectively. We investigate these classes and show that the relevant determining problems are intractable in general. [4]2:00-4:00pm, 26/Sep/2006:Kolmogorov complexity and the recursion theorem. Speaker: Merkle Wolfgang (University of Heidelberg, Germany). [5] 2:00-4:00pm, 10/Oct/2006:Interpreting Structures in R. E. Degrees. Speaker: Wei Wang. Interpreting in a structure M another structure N is a model theoretic technique to reduce properties of some kind of structures to those of another kind, e.g. decidability/undecidability, definability, rigidity. Investigations of "big pictures" of degree structures always involve such technique. We will review two variations in r.e. degrees, namely Harring-Shelah coding and Slaman-Woodin coding, and a shortcoming claimed by Nies of known codings. Finally we will suggest a way to walk around this shortcoming, though our solution does not lead to any valuable insight. To this end we will briefly introduce the construction of Harrington-Shelah coding.

21. Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical Logic A PM arithmetical hierarchy is a proper hierarchy, id=3273 WP arithmetical .. edit 03D20 Recursive functions and relations, subrecursive hierarchies http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Mathematics/PlanetMath_Exchan

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations From Wikipedia, the free encyclopedia Wikipedia:WikiProject Mathematics PlanetMath Exchange Jump to: navigation search This page provides a list of all articles available at PlanetMath in the following topic: 03-XX Mathematical logic and foundations This list will be periodically updated. Each entry in the list has three fields: PM WP Status status entries are: Status means PM article N not needed A adequately covered C copied M merged NC needs copying NM needs merging Please update the WP and Status fields as appropriate. if the WP field is correct please remove the qualifier "guess". If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link. If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry. If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable. Don't forget to include the relevant template if you copy over text or feel like an external link is warranted See the main page for examples and usage criteria.

22. Program On Computation Prospects Of Infinity - IMS algorithmic randomness, subrecursive hierarchies from Gentzenstyle proof reducibilities in infinite levels of the Ershov difference hierarchy http://www.ims.nus.edu.sg/Programs/infinity/abstracts.htm

var imgdir = "../../images/"; var urldir = "../../"; Computational Prospects of Infinity (20 Jun - 15 Aug 2005) ~ Abstracts ~ Refuting Downey's conjecture Steffen Lempp University of Wisconsin, Madison, USA « B ack... Seetapun's theorem and related conjectures on the strength of stable Ramsey's theorem for pairs Carl Jockusch, University of Illinois, Urbana-Champaign, USA « B ack... Weak degrees of Pi^0_1 subsets of 2^omega Stephen G. Simpson, Pennsylvania State University, USA Let P,Q subseteq 2^omega be viewed as mass problems, i.e., "decision problems with more than one solution." We say that the mass problem P is weakly reducible to the mass problem Q if, for every solution Y of Q, there exists a solution X of P such that X is Turing reducible to Y. A weak degree is an equivalence class of mass problems under mutual weak reducibility. (Weak degrees are also known as Muchnik degrees.) Let P_w be the set of weak degrees of nonempty Pi^0_1 subsets of 2^omega, partially ordered by weak reducibility. It is easy to see that P_w is a countable distributive lattice. The speaker and others have studied P_w in a series of publications beginning in 1999. Our principal findings are as follows. 1. There is a natural embedding of R_T, the countable semilattice of recursively enumerable Turing degrees, into P_w. This embedding is one-to-one and preserves the partial ordering leq, the semilattice operation v, and the top and bottom elements and 0'. We identify R_T with its image in P_w under this embedding.

23. 03Dxx 03D20, Recursive functions and relations, subrecursive hierarchies. 03D25, Recursively (computably) enumerable sets and degrees 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

24. Unixpeople Dennis Ritchie, B.A. Physics, Harvard 63;Ph.D. Appl. Math, Harvard 68 (diss on subrecursive hierarchies of functions);BL 68, C, fork-exec, set-userid, db, http://www.princeton.edu/~mike/unixpeople.htm

"In the Beginning: Unix at Bell Labs" Name Education, Experience Contributions to Unix Ken Thompson B.Sc., M.Sc. EE, Berkeley 65, 66; BL 66- B, bas, Fortran (with Ritchie), ed, roff, sort, grep, uniq, plot, sa, dd Dennis Ritchie B.A. Physics, Harvard 63;Ph.D. Appl. Math, Harvard 68 (diss on subrecursive hierarchies of functions);BL 68- C, fork-exec, set-userid, db, ed, I/O stream in v8; (with Thompson) fc (fortran iv); (with Johnson), port to Interdata Joe Osanna n/troff Bob Morris typo, math library, primes, factor, crypt (with Cherry) dc-bc Doug McIlroy B.E.P. Eng'g Physics, Cornell 54; Ph.D. Math, MIT 59; BL 58- tmg, speak, diff, join, look. dict, spell Lorinda Cherry M.S. Computer Science, Stevens 69 eqn (startup), parts Steve Johnson yacc, lint, portable C, spell Lee McMahon B.A., M.A. St. Louis University; Ph.D. Psychology, Harvard; BL 63-89 comm, qsort, sed, grep, index, cref, cu, architect for Datakit Brian Kernighan A.M., Ph.D. EECS, Princeton 66, 69 name UNIX, notion of tools, ratfor, eqn, awk, pic. dvi troff Steve Bourne adb, Bourne shell

25. Home Page Of Georg Moser On the other hand I ve worked on ordinal proof theory, in particular subrecursive hierarchies, hierarchy comparison theorems and Hilbert s epsilon calculus. http://cl-informatik.uibk.ac.at/~georg/

georg moser's homepage personal data name Georg Christian Moser affiliation Computational Logic Group Institute of Computer Science address University of Innsbruck Technikerstrasse 21a, 2. OG (3N01) A-6020 Innsbruck, Austria contact office hours: Monday 13:00-15:00 (no office hours from October 8 till December 10) tel: ++43 (0) 512 5076434 email: georg.moser@uibk.ac.at Since June 2004, I'm research assistant at the Computational Logic Group at the University of Innsbruck , Austria. I received my education at the Vienna University of Technology and at the University of Leeds. My PhD-thesis supervisor was Matthias Baaz and I defended my thesis on Term Induction in June 2001. The supervisor of my master thesis (MSc by Research) at Leeds was Stanley Wainer. My master thesis supervisor at the Vienna University of Technology was Alexander Leitsch. Formerly I have been a Marie-Curie Fellow research interests Keywords: Term Rewriting, Complexity, Proof Theory, and Logic. Term rewriting is a conceptual simple, but powerful abstract model of computation. The foundation of rewriting is equational logic and TRSs are conceivable as sets of directed equations. In order to assess the complexity of a TRS it is natural to look at the maximal length of derivation sequences. This viewpoint gives rise to the study of the derivational complexity of TRSs, a topic that lies at the heart of my research interests. The gist of proof theory is the question whether a proof can tell us more than the truth of a statement. I have done some work on Generalisations of Proofs and considered questions which are loosely grouped around so-called Kreisel's conjecture. On the other hand I've worked on ordinal proof theory, in particular subrecursive hierarchies, hierarchy comparison theorems and Hilbert's epsilon calculus.

26. RAND | Reports & Bookstore | Research Memoranda Random Sets in subrecursive hierarchies. icon Full Document. RealTime Recognition of Handprinted Text Program Documentation. icon Full Document http://www.rand.org/pubs/research_memoranda/index7.html

Optimum graphic presentation of this site requires a modern standards-friendly browser. The browser or PDA you are using may not display exactly as intended, but you will still be able to access all of our content. For more information, see About This Site . Why upgrade? Click here to see how this site's homepage displays with a modern browser. About RAND Annual Report Quality Standards Organizational Structure ... RAND Classics About RAND Reports Bookstore Overview - Catalogs - Ordering Information - Series Overview ... Information for Educators Online Reading Commentary Issue Papers Research Briefs RAND Journal of Economics var addthis_pub = 'Kenl'; Search All Documents Or Browse by Category: Choose a Category Latest Releases The Arts Child Policy Civil Justice Education International Affairs Latin America Methodology National Security Public Safety Substance Abuse Security Infrastructure RAND Classics Browse by Author A B C D ... Z Browse by Document Series: Choose a Series Commercial Books Conference Proceedings Corporate Publications Dissertations Documented Briefings Library Reprints Monographs Occasional Papers Reprints Research Briefs Selected Bibliographies   (Technical) Reports Testimonies Legacy Series CAE Documents Drafts (Unrestricted) Documents Issue Papers Joint Notes:   (Education)   (Soviet) Joint Reports:   (Education)   (Health)   (Immigration)   (Soviet) Monograph/Reports Notes Occasional Papers:   (Education)   (Soviet) Papers RAND Europe Docs Reports Research Memoranda Special Memoranda White Papers Subject Area Bibliographies Research Memoranda

27. The Mathematics Genealogy Project - Joel Robbin Dissertation subrecursive hierarchies. Advisor Alonzo Church. Student(s) Click here to see the students listed in chronological order. http://genealogy.math.ndsu.nodak.edu/id.php?id=8036

28. Department Of Mathematics And Statisitcs - Faculty Members In Pure Math Ordinary and higher recursion theory (computability), subrecursive hierarchies, computational complexity. F. van Breugel, Ph.D. (V.U. Amst.). http://www.math.yorku.ca/new/people/math.htm

Faculty members in Pure Math Section and their research interests ALGEBRA R.G. Burns, Ph.D. (A.N.U.). Combinatorial group theory, general group theory. Y. Gao, Ph.D. ( Saskatchewan). Infinite dimensional Lie algebras, representation theory, vertex operators, homology of algebras, Lie algebras associated with the other nonassociative structures, mathematical physics. M. Zabrocki, Ph.D. ( California at San Diego). Algebraic combinatorics. See also S.D. Promislow (under Analysis); J.M.N. Brown (under Geometry); J. Steprans and W. Tholen (under Foundations); and N. Bergeron (under Combinatorics). ANALYSIS P.C. Gibson, Ph.D. ( Calgary). Applied harmonic analysis (time-frequency analysis and applications to seismic imaging, PDE and signal processing), inverse problems (matrix analysis, orthogonal polynomials, discrete geometry and applications to oscillating systems). M.E. Muldoon, Ph.D. ( Alberta). Special functions, ordinary differential equations, approximations and expansions, functional equations. S.D. Promislow, Ph.D. (U.B.C.) F.S.A. Functional analysis, group theory, actuarial mathematics.

29. Homepage For Andreas Weiermann Postdocs involved, Georg Moser and Ingo Lepper. A copy of Lepper s thesis can be found here . 4. subrecursive hierarchies. Postdoc involved, Georg Moser http://cage.rug.ac.be/~weierman/

Homepage for Andreas Weiermann Picture of Alan Woods together with me in Oberwolfach. Picture of the Wiskunde football team (Sportsdagcompetitie place 9 out of 14. We won three out of five games, but do not ask for the total score of goals we made). I like doing math, logic and CS and playing chess (Int. ELO 2265). In my youth I published three chess problems in a refereed chess journal (DSZ). I also like painting and paintings (e.g. by Emil Nolde). In 1981 I painted the following landscape My children and my wife make my life happy. Pictures of my children: Katharina and Sebastian and another one from Sebastian I sympathize with the following: "It is six in the morning. The house is asleep. Nice music is playing. I prove and conjecture." Andreas Weiermann Universiteir Hoofddocent (Heisenberg Stipendiat till 2005) Vakgroep Zuivere Wiskunde en Computeralgebra Ghent University Krijgslaan 281 - Gebouw S22 B9000 Gent Belgiumo tel: +3292644899 fax +3292644993 Teaching 2007/8 Tofolo II S25 (Eerste lesgever: Leo Storme) (first lecturer: Leo Storme) Auditorium Emmy Noether dinsdag (tuesday) 14:30-17:15 Fasenovergangen (Phase transitions) S25 Auditorium Emmy Noether dinsdag (Tuesday) 8:30-12:15 Erste les (first lecture) 26.09.2007

30. Logic Colloquium '99 : Scientific Program Andreas Weiermann (Münster) Proof theory and subrecursive hierarchies. Abstract In the first part we survey how local predicativity style methods can be http://www.cwi.nl/events/1999/lc99/scientific_program.html

Design by Chinaski WorldWide Maintenance by Jan van Eijck and Marc Pauly Timetable Main topics of LC'99 are proof theory, model theory, set theory, recursion theory, and computational logic. Computational logic is the topic of special focus of the conference (but not at the expense of the other main topics). Contributions are presented in three afternoon sessions (see the following timetable). A number of papers are presented only by title Mon 2 Tue 3 Wed 4 Thu 5 Fri 6 Tutorial: Anand Pillay Tutorial: Anand Pillay ... Ieke Moerdijk coffee break Tutorial: Ieke Moerdijk Tutorial: Ieke Moerdijk ... Greg Hjorth coffee break Tutorial: Greg Hjorth Tutorial: Jan Willem Klop ... Jan Willem Klop lunch break Plenary Talk: Lev Beklemishev Plenary Talk: Andrei Morozov ... Deirdre Haskell Evening Reception Evening Lecture: Johan van Benthem Conference Dinner ... N.G. de Bruijn Tutorials Group Actions and Countable Models - Greg Hjorth (Los Angeles) Abstract Some aspects of the study of countable models can be framed in the context of continuous actions of the infinite symmetric group on an appropriate Polish space of countable structures. Following work of Vaught in the 1970s this has lead to a general investigation of the continuous actions of Polish groups on Polish spaces. I will survey the recent work in this area, with emphasis on the still open Vaught conjecture and how ideas from model theory have continued to provide inspiration in the study of general Polish group actions.

31. [FOM] Natural R.e. Degrees The topics are a. algorithmic randomness. b. reverse mathematics. c. subrecursive hierarchies. d. computational complexity. 6. http://cs.nyu.edu/pipermail/fom/2005-February/008809.html

[FOM] natural r.e. degrees Stephen G Simpson simpson at math.psu.edu Sun Feb 27 22:32:34 EST 2005 Previous message: [FOM] Extending the Language of Set Theory Next message: [FOM] reply to Gordeev Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... http://www.math.psu.edu/simpson/papers/. Previous message: [FOM] Extending the Language of Set Theory Next message: [FOM] reply to Gordeev Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

32. HeiDOK 03D20 Recursive functions and relations, subrecursive hierarchies ( 0 Dok. ) 03D25 Recursively (computably) enumerable sets and degrees ( 0 Dok. http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03D&anzahl

33. Karl-Heinz Niggl S Home Page subrecursive functions on partial sequences, (AML 99) (APAL 95); subrecursive hierarchies on the partial continuous functionals, (PhD thesis) http://eiche.theoinf.tu-ilmenau.de/~niggl/index.html

34. MathNet-Mathematical Subject Classification 03D20, Recursive functions and relations, subrecursive hierarchies. 03D25, Recursively enumerable sets and degrees. 03D30, Other degrees; reducibilities http://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

35. Information Technology Ph.D. universal Turing machines; unsolvable problems; time and space complexity of computations; NPcompleteness problems; subrecursive hierarchies. http://www.uncc.edu/gradmiss/2004GradCatalog/InformationTechnologyPhD-04-05Catal

INFORMATION TECHNOLOGY College of Information Technology CARC 316 http://www.coit.uncc.edu Degree Ph.D. Program Director Dr. Keh-Hsun Chen Graduate Faculty Gail-Joon Ahn, Assistant Professor C. Michael Allen, Professor Keh-Hsun Chen, Professor Bei-Tseng Chu, Professor W. Douglas Cooper, Professor Teresa Dahlberg, Associate Professor Jianping Fan, Assistant Professor Mirsad Hadzikadic, Associate Professor Larry Hodges, Professor Moutaz Khouja, Professor Ram Kumar, Associate Professor Seok-Won Lee, Assistant Professor Zhaoyu Liu, Assistant Professor Lawrence Mays, Professor Zbigniew Michalewicz, Professor Taghi Mostafavi, Associate Professor Kayvan Najarian, Assistant Professor John O’Malley, Assistant Professor Sungjune Park, Assistant Professor Baba Prasad, Assistant Professor Anita Raja, Assistant Professor Zbigniew Ras, Professor Stephanie Robbins, Associate Professor Cem Saydam, Professor Min Shin, Assistant Professor Mike Smith, Assistant Professor Antonis Stylianou, Associate Professor Chandrasekar Subramaniam, Assistant Professor Kalpathi Subramanian, Associate Professor

36. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection functions and relations, subrecursive hierarchies recursive 03D20 functions and stability; attractors, repellers Lyapunov 37B25 http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_22.htm

functions # properties of functions # properties of functions # properties of functions # quasi-analytic and other classes of functions # quaternion and other division algebras: arithmetic, zeta functions # rate of growth of arithmetic functions # rate of growth of functions, orders of infinity, slowly varying functions # rational functions # real 26-XX functions # real- or complex-valued set functions # real-analytic functions # real-analytic sets, complex Nash functions # real-valued functions # real-valued functions # relations with algebraic geometry, complex analysis, special functions # representation functions # representation and superposition of functions # rings and algebras of continuous, differentiable or analytic functions # scalar and vector Lyapunov functions # set-valued functions # spaces and algebras of analytic functions # spaces of vector- and operator-valued functions # special functions # special 33-XX functions # special families of functions # special sets defined by functions # specific types of complex variable functions # specific types of real variable functions # spherical functions # switching theory, application of Boolean algebra; Boolean

37. List KWIC DDC And MSC Lexical Connection relations, subrecursive hierarchies recursive functions and 03D20 relationship to integrable systems 14H70 relationship to Lie algebras and finite simple http://www.mi.imati.cnr.it/~alberto/dml_11_43.htm

reflexivity and semi-reflexivity refraction region # D region # E region # F region # infrared region # ultraviolet region # visible regions # lattice points in specified regions # tolerance and confidence regions # tolerance and confidence regions xxxx # standard subdivisions of spectral regions; philosophy and theory # spectral register sequences and sequences over finite alphabets # shift regression # general nonlinear regression # linear regression # nonparametric regression analysis regression; shrinkage estimators # ridge regular figures, division of spaces # polyhedra and polytopes; regular local rings regular neighborhoods regular rings and generalizations # von_Neumann regular semigroups regular, Gorenstein, Cohen - Macaulay rings, etc.) # homological conditions on rings (generalizations of regular, normal, perfectly or collectionwise normal, etc.) # higher separation axioms (completely regularity of generalized solutions regularity of mappings # boundary regularity of measures, etc.) # set functions and measures on topological spaces ( regularity of solutions regularity of solutions regularity of solutions regularity of solutions of PDE # smoothness and regularization # improperly posed problems;

38. HK -= [Hacker Kulture] =- The subject of my 1968 doctoral thesis was subrecursive hierarchies of functions. My undergraduate experience convinced me that I was not smart enough to be http://www.dvara.net/HK/linkguru.asp

HK = [ Faqs Archive Community Map ... Link ] = HK Newsletter MailingList Blog Updates ... Torna al Lin-K-Menu HEX2005 - Hacking EXtreme 2005 - The International Hacker Open Air Gathering August 2005, The Netherlands Technology, Art, Culture and Politics Hack-Tic Magazine Archive (1989-1994) A gennaio del 1989 esce il primo numero della rivista olandese "Hack-Tic" (Darmstadt, Olanda, www.hacktic.nl/index.html), tra i cui fondatori vi sono Rop Gonggrijp and Paul Jongsma. HackTic contiene articoli sull'hacking, il phreaking, i virus, ed altro. RICHARD STALLMAN Personal Home Page This is the personal web site of Richard Stallman. The views expressed here are my personal views, not those of the Free Software Foundation or GNU Project. For their views and for information about them, see www.gnu.org. THE JARGON FILE A comprehensive compendium of hacker slang The site has recently moved to a new host and the URL has changed. All old requests should continue to work but you should update your bookmarks and scripts to use the new address as soon as possible: jargon.watson-net.com. This will help me track usage stats much better than before. Thanks and sorry for any inconvenience. You can find out more about The Jargon File on the official Jargon File Resources page. Go there for information about adding or changing entries, quoting the file, or ordering the printed version from MIT Press.

39. Infinities And Infinitesimals - Sci.math.research | Google Groups functions in subrecursive hierarchies, computable analysis, and that sort of stuff in general, are studied? Aatu Koskensilta (aatu.koskensi @xortec.fi) http://groups.google.co.vi/group/sci.math.research/msg/e152d7fc453697ff

Help Sign in sci.math.research Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Infinities and infinitesimals The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful Aatu Koskensilta View profile More options Jun 9, 9:30 am Newsgroups: sci.math.research From: Date: Sat, 9 Jun 2007 13:30:03 +0000 (UTC) Local: Sat, Jun 9 2007 9:30 am Subject: Re: Infinities and infinitesimals Reply to author Forward Print View thread ... Find messages by this author On 2007-06-08, in sci.math.research, Norman Wildberger wrote: You are aware, surely, of the existence of the thriving field of proof theory and recursion theory, where ordinal notations, fast growing recursive functions in subrecursive hierarchies, computable analysis, and that sort of stuff in general, are studied? Aatu Koskensilta (aatu.koskensi @xortec.fi) "Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

40. Infinities And Infinitesimals - Sci.math.research | Google Groups recursive functions in subrecursive hierarchies, computable analysis, and that sort of stuff in general, are studied? Of course, he probably isn t. http://groups.google.lk/group/sci.math.research/msg/788da1afb229891b

Help Sign in sci.math.research Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Infinities and infinitesimals The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful tc...@lsa.umich.edu View profile More options Jun 11, 7:00 am Newsgroups: sci.math.research From: tc @lsa.umich.edu Date: Mon, 11 Jun 2007 01:30:06 +0000 (UTC) Local: Mon, Jun 11 2007 7:00 am Subject: Re: Infinities and infinitesimals Reply to author Forward Print View thread ... Find messages by this author Of course, he probably isn't. But I'm not sure that that is the right direction to point him in. As you know, it's pretty common nowadays to run into folks who are suspicious of infinite sets and uncomputable reals and so forth. They typically complain that such concepts are "metaphysical" (though they have no qualms about metaphysical concepts such as symbols, strings, computation, etc., and usually aren't philosophically sophisticated

41. September 2006 - Posts - Norman Sasono The subject of my 1968 doctoral thesis was subrecursive hierarchies of functions.” He added “My undergraduate experience convinced me that I was not smart http://geeks.netindonesia.net/blogs/norman/archive/2006/09.aspx

Sign in Join Help Search Norman Sasono Beauty is the first test: there is no permanent place in the world for ugly Mathematics – G.H. Hardy See also: Other Geeks@INDC Home Contact About ... Comments RSS Recent Posts I just found a Blackhole Speaking at my almamater, IPB Donald E. Knuth Facts Microsoft Student Partners, New Bloggers, Future Technology Leaders ... Richard M. Stallman, Linus Torvalds, and Donald E. Knuth Tags "Orcas" .NET Agile Development Algorithm ... Wolfram Research Navigation Home Blogs Forums Photos ... Downloads About Me My Profile Intimedia Archives December 2007 (8) November 2007 (6) October 2007 (6) September 2007 (7) ... December 2004 (2) September 2006 - Posts Algorithm is a general purpose mental tool "A person well-trained in computer science knows how to deal with algorithms; how to construct them, manipulate them, analyze them. This knowledge is preparation for much more than writing good computer programs; it is a general purpose mental tool that will be a definite aid to the understanding of other subjects, whether they be chemistry, linguistics, or music, etc. The reason for this may be understood in the following way: It has been often been said that a person does not really understand something until after teaching it to someone else. Actually, a person does not really understand something

42. MPIM - Seminar Talks almost everywhere domination, hyperarithmeticity, resourcebounded computational complexity, Kolmogorov complexity, and subrecursive hierarchies. http://www.mpim-bonn.mpg.de/Events/This Year and Prospect/Trimestre on methods o

43. Happenings After a doctoral dissertation on subrecursive hierarchies of functions, Ritchie joined Bell Telephone Laboratories, working on the design of computer http://doi.ieeecomputersociety.org/10.1109/MAHC.1995.10012

var sc_project=2763585; var sc_invisible=0; var sc_partition=28; var sc_security="3c678009"; var addtoLayout=0; var addtoMethod=0; var AddURL = escape(document.location.href); // this is the page's URL var AddTitle = escape(document.title); // this is the page title Advanced Search CS Search Google Search Home Digital Library Podcasts Site Map ... Table of Contents Abstract Summer 1995 (Vol. 17, No. 2) pp. 55-61 Happenings Geoffrey Bowker Full Article Text: DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MAHC.1995.10012 Send link to a friend Abstract The Happenings department reports on past, present, and future events of interest to the history of computing. These events include conferences, appropriate sessions from meetings, exhibits, projects, awards, publications, collections, general memorabilia, and important dates in the history of computing.Contributions to the department are encouraged and should consist of a description or report of the event, highlighting its specific relevance. Back to Top Additional Information Citation: Geoffrey Bowker, "Happenings,"

44. One Man Hacking: Yet Another Math Milestone The subject of my 1968 doctoral thesis was subrecursive hierarchies of functions. Kernighan is a computer Science Prof at Cambridge. http://ravimohan.blogspot.com/2006/02/yet-another-math-milestone.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=14853042"); One Man Hacking Ravi Mohan's Blog Tuesday, February 21, 2006 Yet Another Math Milestone A few days ago, I discovered an error in the mathematics of a paper (on neural network optimization) being prepared for publication by a very eminent scientist. My drawing attention to this discrepancy in the proof has led to a total recasting of the approach to the problem and I will be now listed as a co-author of the paper. Hmm yeah. Whatever. So how is this significant? Well this is the first time I have used my skill in mathematics (vs my skill in programming) to contribute significantly to a scientific effort. In an old blog post I had theorised that the acquisition of "mathematical thinking" would follow a four step path. I said .. the first step in mastering math is be to learn to read the notation. just like learning the syntax of a new programming language the second is to grasp the reality expressed by the notation at a gut level , like understanding the paradigm and patterns lying underneath a programming language , like ,say ,beginning to grok "oo"

45. Computing And Information Technology Interactive Digital Educational Library Rep Mathematical logic and foundations Computability and recursion theory Recursive functions and relations, subrecursive hierarchies. (no description) http://www.citidel.org/?op=cbrowse&scheme=MSC2000&category=03-XX:03Dxx:03D20

46. RDF Description Of A Note On Comparison Of Subrecursive Inf. Process. Lett. A Note on Comparison of subrecursive hierarchies. A Note on Comparison of subrecursive hierarchies. 1971. http://www4.wiwiss.fu-berlin.de/dblp/data/record/journals/ipl/Tsichritzis71

47. PCC 06 - Preliminary Program Mathias Barra, On some small subrecursive hierarchies. Ulrich Berger, Strong normalisation via domaintheoretic computability predicates http://pcc.w3.rz.unibw-muenchen.de/program.html

PCC 06 - Preliminary Program The time for each talk is 45 min, including (at least) 5 min for discussion. A preliminary schedule can be found below Speaker Title Mathias Barra ... Closing

48. General General Mathematics Mathematics For Nonmathematicians 68Q17 Recursive functions and relations, subrecursive hierarchies Recursively (computably) enumerable sets and degrees Other Turing degree structures http://amf.openlib.org/2001/msc2000.xsd

49. PlanetMath: Primitive Recursive Function AMS MSC, 03D20 (Mathematical logic and foundations Computability and recursion theory Recursive functions and relations, subrecursive hierarchies) http://planetmath.org/encyclopedia/PrimitiveRecursive.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About primitive recursive function (Definition) Notation and Terminology , where for each . For each , and for each . The functions and are the zero and successor functions, respectively; the functions are the projection functions. Definition (Primitive Recursive Function The set, PR primitive recursive functions is the smallest subset of such that: for each and is closed under composition If is closed under primitive recursion If , where for and "primitive recursive function" is owned by ratboy full author list owner history view preamble View style: HTML with images page images TeX source Other names: primitive recursive function Attachments: characterization of primitive recursive functions of one variable (Theorem) by rspuzio Log in to rate this entry.

50. BibTeX Bibliography Infoproc1970.bib Toronto, Canada , keywords = comparison; computability and decidability; low level complexity classes; subrecursive hierarchies , treatment = T http://www.math.utah.edu/pub/tex/bib/infoproc1970.html

http://www.math.utah.edu/~beebe beebe at math.utah.edu http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/ %%% %%% with tables of contents from 1994 (Volume %%% 49) to date. All of the data at that site %%% for volumes 4968 has been merged into %%% this file. %%% %%% Abstracts and full text of articles are %%% available electronically to qualified %%% subscribers, which includes members of %%% organizations with institutional %%% subscriptions; most large universities should %%% fall in this group. For details, visit %%% %%% http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/?menu ack-nhfb beebe@math.utah.edu beebe@acm.org beebe@ieee.org http://www.math.utah.edu/~beebe/ j-INFO-PROC-LETT pub-SUCSLI pub-SUCSLI:adr Stacey:1971:RVM j-INFO-PROC-LETT ack-nhfb Duncan:1971:PSS j-INFO-PROC-LETT ack-nhfb Maurer:1971:SPG j-INFO-PROC-LETT ack-nhfb Zissos:1971:PSR j-INFO-PROC-LETT ack-nhfb Henhapl:1971:RTM j-INFO-PROC-LETT ack-nhfb Merret:1971:GPM j-INFO-PROC-LETT ack-nhfb Karlgren:1971:SRS j-INFO-PROC-LETT ack-nhfb Knuth:1971:ENA j-INFO-PROC-LETT Knuth:1971:NAG ack-nhfb Knuth:1971:NAG j-INFO-PROC-LETT Knuth:1971:ENA ack-nhfb Hopcroft:1971:ADI j-INFO-PROC-LETT ack-nhfb Salton:1971:PII j-INFO-PROC-LETT ack-nhfb Tsichritzis:1971:NCS j-INFO-PROC-LETT ack-nhfb Caviness:1971:ELC j-INFO-PROC-LETT ack-nhfb Milgram:1971:NSC

51. Selected Talks (Lars Kristiansen) ComplexityTheoretic hierarchies Copenhagen Programming Language Seminar, A jump operator on honest subrecursive degrees. ASL Logic Colloquium 95, 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.

52. Talk 1998, August 24 28 A finite hierarchy of recursively enumerable real numbers, 1993, November 15 The hierarchies of subrecursive functions. http://www-sst.informatik.tu-cottbus.de/~wwwti/zheng/talk.html

Some of My Talks 2004, December 13: Eine Berechenbarkeitstheorie reeller Zahlen BTU Cottbus (Folien pdf 2004, November 15: On the Hierarchy of Delta2 Real Numbers, RNC'6, Dargstuhl (Slides pdf 2004, November 1: Alternative Zugänge zum Unvollständigkeitssatz von Gödel BTU Cottbus (Folien pdf 2004, August, 18: On the Extensions of Solovay-Reducibility COCOON 2004, Jiju, Korea (Slides, PDF 2003, September 30: Effective analysis and the applications , Jiangsu University, China. 2003, September 25: Various computabilities of real numbers , Nanjing University, China. 2003, Feberay 28: On the effective Jordan decomposability, STACS 2003, Berlin 2003, July 7-12: On the monotonic computability of semi-computable real numbers, DMTCS 2003, Dijon, France) 2003, August 28 - 30: h -Monotonically computable real numbers, CCA 2003, Cincinnati, USA 2003, July 25-28: On the divergence bounded computable real numbers, COOCON, Big Sky, USA 2002, August 15-17: Computable Real Functions of Bounded Variation and semi-Computable Real Numbers, COCOON 2002, Singapore

53. An Analog Characterization Of The Subrecursive Functions An Analog Characterization of the subrecursive Functions. Author(s) then it can compute functions on any given level of the Grzegorczyk hierarchy. http://www.santafe.edu/research/publications/wpabstract/200001005

Quick Links... Bulletin Library People Summer Schools Working Papers Visiting SFI News Contact Us Home Contact Us ... Overview SFI Working Paper Abstract Title: An Analog Characterization of the Subrecursive Functions Author(s): Files: gzipped postscript postscript pdf Paper #: Abstract: We study a restricted version of Shannon's General Purpose Analog Computer in which we only allow the machine to solve linear differential equations. This corresponds to only allowing local feedback in the machine's variables. We show that if this computer is allowed to sense inequalities in a differentiable way, then it can compute exactly the elementary functions. Furthermore, we show that if the machine has access to an oracle which computes a function $f(x)$ with a suitable growth as $x$ goes to infinity, then it can compute functions on any given level of the Grzegorczyk hierarchy. More precisely, we show that the model contains exactly the $n$th level of the Grzegorczyk hierarchy if it is allowed to solve $n-3$ nonlinear differential equations of a certain kind. Therefore, we claim that there is a close connection between analog complexity classes, and the dynamical systems that compute them, and classical sets of subrecursive functions. Credits

54. An Analog Characterization Of The Subrecursive Functions then it can compute functions on any given level of the Grzegorczyk hierarchy. systems that compute them, and classical sets of subrecursive functions. http://ideas.repec.org/p/wop/safiwp/00-01-005.html

This file is part of IDEAS , which uses RePEc data Papers Articles Software Books ... Help! An Analog Characterization of the Subrecursive Functions Author info Abstract Publisher info Download info ... Statistics Author Info Manuel Lameiras Campagnolo Cristopher Moore Jos© F©lix Costa Abstract We study a restricted version of Shannon's General Purpose Analog Computer in which we only allow the machine to solve linear differential equations. This corresponds to only allowing local feedback in the machine's variables. We show that if this computer is allowed to sense inequalities in a differentiable way, then it can compute exactly the elementary functions. Furthermore, we show that if the machine has access to an oracle which computes a function f(x) with a suitable growth as x goes to infinity, then it can compute functions on any given level of the Grzegorczyk hierarchy. More precisely, we show that the model contains exactly the nth level of the Grzegorczyk hierarchy if it is allowed to solve n-3 non-linear differential equations of a certain kind. Therefore, we claim that there is a close connection between analog complexity classes, and the dynamical systems that compute them, and classical sets of subrecursive functions. Download Info To our knowledge, this item is not available for download

55. Book Computability Theory, Maths For Engineers, Lavoisier Publishers computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. recent work in computability theory has focused on http://www.lavoisier.fr/notice/gb402380.html

Search on All Book CD-Rom eBook Software The french leading professional bookseller Description Approximate price Computability theory Author(s) : COOPER S. Barry Publication date : 09-2003 Language : ENGLISH Status : In Print (Delivery time : 12 days) Description Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. Summary Subject areas covered: Mathematics and physics Applied maths and statistics Maths for engineers New search Your basket Information New titles BiblioAlerts E-books Customer services Open an account Ordering non-listed items Order tracking Help Lavoisier.fr