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Topic: Recursion theory

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	Recursion theory - Wikipedia, the free encyclopedia
		Recursion theory, or computability theory, is a branch of mathematical logic dealing with generalizations of the notion of computable function, and with related notions such as Turing degrees and effective descriptive set theory.
		Basic to recent developments in the subject is the theory of relative computability.
		Following the early work of Kleene and Post, its study has formed one of the central areas of research in computability theory over the last fifty years, yet it is only recently that some of the deeper patterns and interrelationships have emerged.
	en.wikipedia.org /wiki/Recursion_theory (449 words)

	Recursion
		Recursion simply means applying a function as a part of the definition of that same function.
		Recursion on large data structures tends to eat up memory so if you are short of memory, or have very large data structures to process the more complex conventional code may be safer.
		Recursive functions must have a non-recursive terminating condition or an infinite loop will occur.
	www.freenetpages.co.uk /hp/alan.gauld/tutrecur.htm (1021 words)

	[No title]
		Historically the theory of computability has been mainly couched in terms of recursive functions, a collection of functions built from a small base by means of a small number of constructors.
		Different recursion combinators, and indeed a whole hierarchy of them, are well known in the literature on lambda calculus and combinatory logic; see for example {Barendregt84}, {Henson87}, {Revesz88}.
		Recursion then occurs respectively on the predecessor or the rest, and the rudimentary rec2-part typically combines the results.
	www.latrobe.edu.au /philosophy/phimvt/joy/j05cmp.html (6457 words)

	Recursion Theory F2003
		We focused our attention on the fundamental results of Recursion Theory: the Normal Form, Enumeration, Parametre, and Recursion theorems, as reinforced by Homework Exercises.
		Recursion Theory is the study of computability properties of objects like functions and sets of natural numbers, sets of reals etc. It also addresses decidability of problems naturally occurring in mathematics or logic.
		In the sping semester of 2003 we plan to hold a seminar on Recursion Theory.
	www.itu.dk /people/volodya/RTF2003.html (1293 words)

	Bounded Queries in Recursion Theory
		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.
		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).
		In Part A basic notions and results from recursion theory and bounded queries are introduced together with some notations used in the book.
	www.ici.ro /ici/revista/sic2000_4/art15.htm (712 words)

	Logic, 8
		Recursively enumerable can be thought of as being able to find the positive cases, but not the negative ones – i.e., one cannot falsify some inclusion in the set, since the program may not converge.
		Recursive implies falsifiability, which is intuitively a close relative of decidability.
		This contradicts the assumption that B was not recursive.
	www.media.mit.edu /physics/pedagogy/babbage/texts/rt.html (8591 words)

	Recursive Function Theory Newsletter
		The first issue of the Recursive Function Theory Newsletter was mailed from Berkeley in April of 1972.
		The original aim, which was maintained for over twenty years, was to provide, for the increasingly far-flung recursion theoretic community, access to the latest developments in the subject.
		The Recursion Theoretic era, during which much of the technical and conceptual basis for 21st century Computability Theory was established, can be found reflected in the pages of the Newsletter.
	www.amsta.leeds.ac.uk /pure/staff/cooper/rec.html (440 words)

	Category methods in recursion theory., J. Myhill
		[3] Jacob Dekker and John Myhill, Recursion theory, to be published by North Holland.
		[8] A. Kuznecov and B. Trahtenbrot Investigation of partial recursive oparators by means of the otheoryf Baire space, Proc.
		[19] Clifford Spector, On degrees of recursive unsolvability, Ann.
	projecteuclid.org /getRecord?id=euclid.pjm/1103036931 (267 words)

	A K Peters, Ltd. - Recursion Theory (Site not responding. Last check: 2007-10-07)
		This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory.
		The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests.
		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 recursion theory.
	www.akpeters.com /product.asp?ProdCode=1497 (121 words)

	Recursion: Index (Site not responding. Last check: 2007-10-07)
		Let's explore the concepts of recursion and recurrences.
		Recursion often allows easily expressing complex procedure, with often impressive results.
		We examine recursion through two specific examples: the Towers of Hanoi puzzle and exponentiation.
	www-2.cs.cmu.edu /~cburch/survey/recurse (45 words)

	Amazon.com: Classical Recursion Theory, Volume II (Studies in Logic and the Foundations of Mathematics): Books: P. ... (Site not responding. Last check: 2007-10-07)
		As a first approximation, we introduce static complexity measures in an abstract way as follows: given an acceptable system of indices {e}e for the partial recursive functions (see II.5.2), we call a static complexity measure any total recursive function m, and call complexity or size of e the number m(e).
		He is at his best when relating recursion theory to science, philosophy, and other branches of math.
		The book as a whole is not very unified and it doesn't clearly indentify and relate the central ideas of recursion theory, so it wouldn't make a good introductory text.
	www.amazon.com /exec/obidos/tg/detail/-/044450205X?v=glance (848 words)

	CIDEC Library: Shoenfield * Recursion Theory (Site not responding. Last check: 2007-10-07)
		This is an introduction to recursive functions intended for graduate students.
		It presupposes some mathematical maturity and a slight aquaintance with some important topics, such as group theory and topology.
		It introduces the main topics of recusion theory, such as hierarchy theory, RE sets, and undecidable theories, without going very deeply into any of them.
	www.cs.ioc.ee /yik/lib/1/Shoenfield1.html (102 words)

	About "Introduction to Logic and Recursion Theory" (Site not responding. Last check: 2007-10-07)
		Sacks at M.I.T. in the spring of 1998, organized and reinterpreted.
		Propositional Calculus; First-Order Logic; Towards Completeness and Consistency; Recursion Theory — compare this to Sipser’s Computation, Part II; Clarity is of the essence; Post's Problem.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/view/17235.html (51 words)

	Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers (Site not responding. Last check: 2007-10-07)
		Book Description: 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number.
		Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees.
		Included are a number of applications to logic (in particular GÃ¶del's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
	isbn.nu /0444894837 (433 words)

	Amazon.ca: Recursion Theory for Metamathematics: Books (Site not responding. Last check: 2007-10-07)
		The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of
		It is both an introduction to the theory and a presentation of new results in the field.
		Be the first person to review this item.
	www.amazon.ca /exec/obidos/ASIN/019508232X (299 words)

	Past Colloquium and Seminar Speakers
		Entropy and Knots (this is part of the presentations of the "Knot Theory" course).
		The Kauffman bracket skein algebra of a surface cross interval is finitely generated.
		The structure of the Kauffman bracket skein algebra of torus cross interval and punctured torus cross interval.
	www.gwu.edu /~math/colloquiahistory.html (4115 words)

	Amazon.com: Recursion Theory for Metamathematics (Oxford Logic Guides): Books: Raymond M. Smullyan (Site not responding. Last check: 2007-10-07)
		The Philosophy of Set Theory : An Historical Introduction to Cantor's Paradise (Dover Books on Mathematics) by Mary Tiles
		Computability : An Introduction to Recursive Function Theory by N.
		This work is a sequel to the author's G"odel's Incompleteness Theorems, though it can be read independently by anyone familiar with G"odel's incompleteness theorem for Peano arithmetic.
	www.amazon.com /exec/obidos/tg/detail/-/019508232X?v=glance (522 words)

	LtU Classic Archives (Site not responding. Last check: 2007-10-07)
		Joy is a functional programming language which is not based on the application of functions to arguments but on the composition of functions.
		Joy is a very pretty creation indeed, unifying many of the things I liked about Forth with functional programming and combinators, two other favorite subjects of mine.
		Isaac Gouy - Re: Recursion Theory and Joy
	lambda-the-ultimate.org /classic/message5521.html (473 words)

	Ordinal Recursion Theory (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		Abstract: this article, we take up the topic of "admissibility spectra", where instead of studying the definability of subsets of a fixed \Sigma 1 -admissible ordinal, we ask: given a set X, which are the ordinals \Sigma 1 -admissible relative to X? (Update)
		0.3: The Axiom of Choice from the Viewpoint of Recursion Theory - Jojgov (1999)
		1 The recursively enumerable ff-degrees are dense (context) - Shore - 1976
	citeseer.ist.psu.edu /335191.html (171 words)

	Citebase - The diagonalization method in quantum recursion theory
		Citebase - The diagonalization method in quantum recursion theory
		Due to the continuity of quantum states, classical diagonalization has to be revised for quantum recursion theory.
		[] H. Rogers, Jr., Theory of Recursive Functions and Effective Computability (MacGraw-Hill, New York, 1967).
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/9412048 (227 words)

	Schedule Special Session: Recursion Theory (Site not responding. Last check: 2007-10-07)
		Lecture: Recent Developments in Recursion Theory I. Downey (Victoria University, New Zealand)
		Talk: On the elementary theory of the Boolean pairs (Delta-Zero n, Delta- Zero m) with n>m.
		Contributed paper: Endomorphisms of the Group of all Recursive Permutations
	www.cs.technion.ac.il /~logic95/rec-schedule.html (175 words)

	Recursion Theory in Set Theory (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		@inproceedings{ slamandidrecursion, author = "Theodore A. Slaman", title = "Recursion theory in set theory", pages = "273--278", url = "citeseer.ist.psu.edu/259441.html" }
		14 Higher Recursion Theory (context) - Sacks - 1990
		Definability In The Recursively Enumerable Degrees - Nies, Shore, Slaman
	citeseer.ist.psu.edu /259441.html (222 words)

	Classical Recursion Theory - SHOP.COM (Site not responding. Last check: 2007-10-07)
		Classical Recursion Theory : The Theory of Functions and Sets of Natural Numbers
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		All other designated trademarks, copyrights and brands are the property of their respective owners.
	www.shop.com /op/aprod-p31925206 (135 words)

	Computability Theory
		Open Questions in Recursion Theory: LaTeX or pdf.
		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.
	www.nd.edu /~cholak/computability/computability.html (128 words)

	03Dxx (Site not responding. Last check: 2007-10-07)
		03D45 Theory of numerations, effectively presented structures, See also {03C57}
		03D50 Recursive equivalence types of sets and structures, isols
		03D60 Recursion theory on ordinals, admissible sets, etc.
	www.ma.hw.ac.uk /~chris/MR/03Dxx.html (75 words)

	Recursion theory - Computer Books
		Click a book link to view all the available details:
		· Recursion Theory for Metamathematics (Oxford Logic Guides, No. 22)
		· Computability : An Introduction to Recursive Function Theory
	www.centrasoft.com /c2/catR_4898.htm (29 words)

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