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Topic: Kleene fixpoint theorem

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	CONK! Encyclopedia: Stephen_Cole_Kleene (Site not responding. Last check: 2007-10-15)
		Kleene was best known for founding the branch of mathematical logic known as recursion theory together with Alonzo Church, Kurt GÃ¶del, Alan Turing and others; and for inventing regular expressions.
		Kleene's standing in mathematical logic is reflected in the proverb "Kleeneliness is next to GÃ¶deliness" among logicians (a pun on "Cleanliness is next to godliness").
		An avid mountain climber, Kleene had a strong interest in nature and the environment and was active in many conservation causes.
	www.conk.com /search/encyclopedia.cgi?q=Stephen_Cole_Kleene (424 words)

	Stephen Cole Kleene - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-15)
		Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science.
		Kleene's standing in mathematical logic is reflected in the proverb "Kleeneliness is next to Gödeliness" among logicians.
		The Kleene Symposium: Proceedings of the Symposium Held June 18-24, 1978 at Madison, Wisconsin, U.S.A. (Studies in logic and the foundations of mathematics)
	encyclopedia.worldsearch.com /stephen_cole_kleene.htm (504 words)

	Kleene algebra - Encyclopedia Glossary Meaning Explanation Kleene algebra (Site not responding. Last check: 2007-10-15)
		A Kleene algebra is a set A together with two binary operations + : A × A → A and · : A × A → A and one function * : A → A, written as a + b, ab and a* respectively, so that the following axioms are satisfied.
		In fact, this is a "free" Kleene algebra in the sense that any equation among regular expressions follows from the Kleene algebra axioms and is therefore valid in every Kleene algebra.
		Kleene algebras were not defined by Kleene; he introduced regular expressions and asked for a set of axioms which would allow to derive all equations among regular expressions.
	www.encyclopedia-glossary.com /en/Kleene-algebra.html (1217 words)

	Encyclopedia: Stephen Cole Kleene (Site not responding. Last check: 2007-10-15)
		Kleenes recursion theorem is a result in computability theory first proved by Stephen Kleene; it allows to construct programs, Turing machines and recursive functions that refer back to their own description.
		In mathematics, a Kleene algebra (named after Stephen Cole Kleene, pronounced clay-knee) is either of two different things: A bounded distributive lattice with an involution satisfying De Morgans laws, and the inequality x∧−x ≤ y∨−y.
		In mathematics, the Kleene fixpoint theorem in order theory states that given any complete lattice L, and a monotone function f : L → L, then the least-fixed point (lfp) of f is.
	www.nationmaster.com /encyclopedia/Stephen-Cole-Kleene (1803 words)

	Stephen Cole Kleene -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-15)
		By providing methods of determining which problems are solvable, Kleene's work led to the study of which functions are (Click link for more info and facts about computable function) computable function.
		The (Click link for more info and facts about Kleene star) Kleene star, (Click link for more info and facts about Kleene's recursion theorem) Kleene's recursion theorem and the Ascending Kleene Chain are named after him.
		Kleene was born in (The state capital of Connecticut; located in central Connecticut on the Connecticut river; a center of the insurance business) Hartford, (A New England state; one of the original 13 colonies) Connecticut, (The army of the United States of America; organizes and trains soldiers for land warfare) USA.
	www.absoluteastronomy.com /encyclopedia/S/St/Stephen_Cole_Kleene.htm (490 words)

	Read about Stephen Cole Kleene at WorldVillage Encyclopedia. Research Stephen Cole Kleene and learn about Stephen Cole ... (Site not responding. Last check: 2007-10-15)
		Kleene was best known for founding the branch of
		Kleene's standing in mathematical logic is reflected in the proverb "Kleeneliness is next to
		An avid mountain climber, Kleene had a strong interest in nature and the
	encyclopedia.worldvillage.com /s/b/Kleene (398 words)

	Encyclopedia: Kleene fixpoint theorem (Site not responding. Last check: 2007-10-15)
		A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions.
		In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set is an element of S which is greater than or equal to any other element of S. The term least element is defined dually.
		Order theory In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point, under some conditions on F that can be stated in general terms.
	www.nationmaster.com /encyclopedia/Kleene-fixpoint-theorem (374 words)

	Yuri Gurevich: Annotated Articles
		Andreas Blass, Benjamin Rossman and the speaker are extending the Small-Step Characterization Theorem (that asserts the validity of the sequential version of the ASM thesis) and the Wide-Step Characterization Theorem (that asserts the validity of the parallel version of the ASM thesis) to intra-step interacting algorithms.
		The theorems are used to explain and sharpen several recent undecidability results related to the corroboration problem, the simultaneous rigid E-unification problem and the prenex fragment of intuitionistic logic with equality.
		A number of famous theorems about first-order logic were disproved in [60] in the case of finite structures, but Lyndon's theorem on monotone vs. positive resisted the attack.
	research.microsoft.com /~gurevich/annotated.html (11831 words)

	Dexter Kozen's Online Publications (Site not responding. Last check: 2007-10-15)
		We study the complexity of reasoning in Kleene algebra and -continuous Kleene* algebra in the presence of extra assumptions; i.e., the complexity of deciding the validity of universal Horn formulas E --> s=t, where E is a finite set of equations.
		However, unlike Kleene algebras, they are not closed under the formation of matrices, which renders them inapplicable in certain constructions in automata theory and the design and analysis of algorithms.
		Kleene algebras are an important class of algebraic structures that arise in diverse areas of computer science: program logic and semantics, relational algebra, automata theory, and the design and analysis of algorithms.
	www.cs.cornell.edu /kozen/papers/default.html (7190 words)

	STEPHEN COLE KLEENE FACTS AND INFORMATION (Site not responding. Last check: 2007-10-15)
		Kleene was best known for founding the branch of mathematical_logic known as recursion_theory together with Alonzo_Church, Kurt Gödel, Alan_Turing_ and others; and for inventing regular_expressions.
		The Kleene_star, Kleene's_recursion_theorem and the Ascending_Kleene_Chain are named after him.
		Kleene's standing in mathematical_logic is reflected in the proverb "Kleeneliness is next to Gödeliness" among logicians (a pun on "Cleanliness is next to godliness").
	www.mrdefine.com /Stephen_Cole_Kleene (367 words)

	Stephen Cole Kleene - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-10-15)
		(Redirected from Kleene, S.C. Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science.
		This page was last modified 01:42, 20 Jun 2005.
		The article about Stephen Cole Kleene contains information related to Stephen Cole Kleene, Biography, Important publications, See also, References and External links.
	www.arikah.net /encyclopedia/Kleene,_S.C. (476 words)

	[No title]
		One consequence ot the S-m-n theorem is the diagonalisation theorem: There is a recursive function taking as argument the Gödel number of a function which takes at least one parameter, and giving as value the Gödel number of the function obtained from the given one by substituting itself for the parameter.
		The recursion theorem traces its ancestry to Epimenides, Russell and Grelling (for
		The above proof of Rice's theorem for Joy is adapted from a proof for recursive functions in {Phillips92}.
	www.latrobe.edu.au /philosophy/phimvt/joy/j05cmp.html (6457 words)

	Abstracts for TYPES 98
		Resolution based theorem provers such as Otter are more powerful in this respect, but have the drawback that they work with normal forms of formulas, so-called clausal forms.
		One novelty is that we use short constructive proofs of Dickson's lemma and Hilbert's basis theorem which are extracted from classical proofs using the techniques of [Coquand 92] based on open induction [Raoult 88].
		We study the dependencies between theorems and definitions in a theory and how they can be exploited in the development and the maintenance of theory.
	www.tcs.informatik.uni-muenchen.de /~types98/abstract.html (3504 words)

	Citations: Fixpoint induction and proofs of program properties - Park (ResearchIndex) (Site not responding. Last check: 2007-10-15)
		The principle of co induction (PCI) is used to prove the extensional equality of two potentially infinite lists from the existence of a certain invariant relating their construction, called a bisimulation.
		Fixpoint induction is based on a variant of Kleene s fixpoint theorem (Theorem 10.13) where the powerset CPO (complete partial order) A) is....
		Theorem 5.8.1 (Park)For any tactic Q, and continuous function from tactics to tactics, F : F (Q) vT Q Gamma X ffl F (X) Delta vT Q : In order to demonstrate equality of recursively defined tactics, it suffices to show refinement in each direction....
	citeseer.ifi.unizh.ch /context/317472/0 (3582 words)

	Kleene fixpoint theorem - Encyclopedia Glossary Meaning Explanation Kleene fixpoint theorem (Site not responding. Last check: 2007-10-15)
		Kleene fixpoint theorem - Encyclopedia Glossary Meaning Explanation Kleene fixpoint theorem.
		Here you will find more informations about Kleene fixpoint theorem.
		The orginal Kleene fixpoint theorem article can be editet
	www.encyclopedia-glossary.com /en/Kleene-fixpoint-theorem.html (120 words)

	Kleene Fixpoint Theorem Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-15)
		Looking For kleene fixpoint theorem - Find kleene fixpoint theorem and more at Lycos Search.
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	www.karr.net /search/encyclopedia/Kleene_fixpoint_theorem (238 words)

	Acta Sci. Math. (Szeged) -- vol. 67. num. 1-2, 2001 (Site not responding. Last check: 2007-10-15)
		One of the central results of the early theory of lattice ordered groups is a theorem due to Ján Jakubik, telling that a maximal convex chain containing the identity element is a direct factor.
		In \cite {bibjac} and \cite {bibosa} there is shown to be many difficulties associated with this problem but the main examples and theorems there concern the Rees quotients of free monoids on small numbers of generators.
		As a consequence, a generalization of Ko and Tan's coincidence theorem is obtained.
	www.acta.hu /Volumes/acta6712.htm (2194 words)

	Corollaries on the fixpoint completion: studying the stable semantics by means of the Clark completion (ResearchIndex) (Site not responding. Last check: 2007-10-15)
		Corollaries on the fixpoint completion: studying the stable semantics by means of the Clark completion (ResearchIndex)
		Corollaries on the fixpoint completion: studying the stable semantics by means of the Clark completion
		Abstract: The xpoint completion x(P) of a normal logic program P is a program transformation such that the stable models of P are exactly the models of the Clark completion of x(P).
	sherry.ifi.unizh.ch /660143.html (773 words)

	Fixpoint Semantics for Logic Programming - A Survey - Fitting (ResearchIndex) (Site not responding. Last check: 2007-10-15)
		Fixpoint Semantics for Logic Programming A Survey (1999)
		Fixpoint semantics for logic programming -- a survey.
		42 Quantitative deduction and its fixpoint theory (context) - van Emden - 1986
	citeseer.ifi.unizh.ch /fitting99fixpoint.html (662 words)

	Computer Science Papers of Andreas R. Blass
		We define their semantics in the framework of ordinary algorithms, and we show that they satisfy the postulates for these algorithms.
		Our main theorem is that all ordinary algorithms, as defined by the postulates, are equivalent to ASMs.
		We prove linear-time hierarchy theorems for random access machines and Gurevich abstract state machines (formerly called evolving algebras).
	www.math.lsa.umich.edu /~ablass/comp.html (3212 words)

	Constructive Versions Of Tarski's Fixed Point Theorems - Cousot, Cousot (ResearchIndex) (Site not responding. Last check: 2007-10-15)
		Abstract: this paper is to give a constructive proof of Tarski's theorem without using the continuity hypothesis.
		The set of fixed points of F is shown to be the image of L by preclosure operations defined by means of limits of stationary transfinite iteration sequences.
		The common fixpoints of a family F = df (f k) k2IN of monotonic functions are described by iterations, given that each pair f k, f...
	citeseer.lcs.mit.edu /cousot79constructive.html (586 words)

	DIMACS Workshop on Applications of Lattices and Ordered Sets to Computer Science
		For example, it is a consequence of the categorical universality of ${\bf V}$ that every monoid may be represented as the endomorphism monoid of each member of a proper class of non-isomorphic algebras each of which belongs to ${\bf V}$.
		That theorem gives a general condition under which protocols that meet some security goal separately are guaranteed still to meet it if run together on the same network.
		We study fixpoints of operators on lattices and bilattices in a systematic and principled way.
	dimacs.rutgers.edu /Workshops/Lattices/abstracts.html (3384 words)

	Stephen Cole Kleene Details, Meaning Stephen Cole Kleene Article and Explanation Guide
		Stephen Cole Kleene Details, Meaning Stephen Cole Kleene Article and Explanation Guide
		He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School in New York, and then a project director at the Naval Research Laboratory in Washington, D.C
		This is an Article on Stephen Cole Kleene.
	www.e-paranoids.com /s/st/stephen_cole_kleene.html (455 words)

	CITIDEL: Viewing 'Automatic synthesis of optimal invariant assertions: Mathematical foundations' (Site not responding. Last check: 2007-10-15)
		The problem of discovering invariant assertions of programs is explored in light of the fixpoint approach in the static analysis of programs, Cousot [1977a], Cousot[1977b]. In section 2 we establish the lattice theoric foundations upon which the synthesis of invariant assertions is based.
		In section 7 we show how difference equations can be utilized to discover the general term of the sequence of successive approximations so that optimal invariants are obtained by a mere passage to the limit.
		In section 8 we show that an approximation of the optimal solution to a fixpoint system of equations can be obtained by strengthening the term of a chaotic iteration sequence.
	www.citidel.org /?op=getobj&identifier=oai:ACMDL:articles.806926 (699 words)

	Ultimate Approximation and Its Application in (ResearchIndex) (Site not responding. Last check: 2007-10-15)
		Abstract: In this paper we study fixpoints of operators on lattices and bilattices in a systematic and principled way.
		The key concept is that of an approximating operator, a monotone operator on the product bilattice, which gives approximate information on the original operator in an intuitive and well-defined way.
		With any given approximating operator our theory associates several di#erent types of fixpoints, including the Kripke-Kleene fixpoint, stable fixpoints and the well-founded fixpoint, and...
	citeseer.lcs.mit.edu /659517.html (493 words)

	ECTS Guide - Department of Informatics
		To cover six central theorems of mathematical logic: Kleene’s enumeration theorem, Godel’s completeness theorem, Church’s undecidability theorem, Tarski’s undefinibility theorem and Godel’s first and second incompleteness theorems.
		The central piece of this section is the above mentioned theorem of Kleene.
		The final section uses results and notions of the previous two sections to prove Church’s undecidability theorem, Tarski’s undefinibility theorem and Godel’s first incompleteness theorem (in the form that no recursive true axiomatization of first-order arithmetic exhausts all first-order truths of arithmetic).
	www.fc.ul.pt /en/informatics2.html (4547 words)

	On Computing the Fixpoint of a Set of Boolean Equations (ResearchIndex) (Site not responding. Last check: 2007-10-15)
		Abstract: This paper presents a method for computing a least fixpoint of a system of equations over booleans.
		The resulting computation can be significantly shorter than the result of iteratively evaluating the entire system until a fixpoint is reached.
		2 A theorem on resolving equations in the space of languages (context) - Leszczyl - 1971
	sherry.ifi.unizh.ch /693167.html (265 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		In many cases a simple syntactic check shows that the closed form of a function, F, can be found immediately.
		The fixed point is simply F(0) where 0 is the least element of the lattice.
		We show that the immediate fixpoint theorem can be applied to a wider class of functions when the lattice elements are monotonic and further improve its applicability by the symbolic manipulation of the functions.
	www.diku.dk /topps/activities/topps-talks/1998/981124 (153 words)

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