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Topic: Kleene algebra

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	WoLLIC'2001 - Title and Abstract of Tutorial Lectures
		Kleene algebra with tests (KAT) is an equational system that captures axiomatically the properties of a natural class of structures arising in logic and computer science.
		Kleene algebra is named for Stephen Cole Kleene (1909-1994), who among his many other achievements invented finite automata and regular sets, structures of fundamental importance in computer science.
		Kleene algebra is the algebraic theory of these objects, although it has many other natural and useful interpretations.
	www.cin.ufpe.br /~wollic/wollic2001/tutorials.html (2078 words)

	Stephen Cole Kleene (Site not responding. Last check: 2007-10-20)
		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.
		By providing methods of determining which problems are solvable, Kleene's work led to the study of which functions are computable.
		An avid mountain climber, Kleene had a strong interest in nature and the environment and was active in many conservation causes.
	www.bidprobe.com /en/wikipedia/s/st/stephen_cole_kleene.html (408 words)

	Kleene algebra
		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.brainyencyclopedia.com /encyclopedia/k/kl/kleene_algebra.html (1160 words)

	Kleene algebra -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		Thus every (A system of symbolic logic devised by George Boole; used in computers) Boolean algebra is a Kleene algebra, but most Kleene algebras are not Boolean algebras.
		Let M be a (Click link for more info and facts about monoid) monoid with identity element e and let A be the set of all (A set whose members are members of another set; a set contained within another set) subsets of M.
		Every (A system of symbolic logic devised by George Boole; used in computers) boolean algebra with operations v and ^ turns into a Kleene algebra if we use v for +, ^ for · and set a* = 1 for all a.
	www.absoluteastronomy.com /encyclopedia/k/kl/kleene_algebra.htm (1240 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-20)
		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.
		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. In 1946, he returned to Wisconsin, becoming a full professor in 1948.
	www.alanaditescili.net /index.php?title=Stephen_Kleene (446 words)

	Algebraic structure (Site not responding. Last check: 2007-10-20)
		Kleene algebra: two binary operations and one unary operator, modeled on regular expressions
		Algebraic structures can also be defined on sets with additional non-algebraic structures, such as topological spaces.
		Every algebraic structure has its own notion of homomorphism, a function that is compatible with the given operation(s).
	www.termsdefined.net /al/algebraic-structure.html (693 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Kleene Algebra is a related algebraic system for calculating with sequential composition, choice and finite iteration.
		The classical application of Kleene algebra is in the theory of formal languages, where it is one of many equivalent approaches to the description of regular languages.
		Papers on theoretical foundation of the calculus of relations and Kleene algebra or on their mechanization are highly welcome.
	www.informatik.uni-kiel.de /~relmics7/cfp.txt (414 words)

	Semiring (Site not responding. Last check: 2007-10-20)
		In abstract algebra, a semiring is an algebraic structure, similar to a ring, but without additive inverses.
		A Kleene algebra is an idempotent semiring R with an additional unary operator * : R → R called the Kleene star.
		Kleene algebras are important in the theory of formal languages and regular expressions.
	www.worldhistory.com /wiki/S/Semiring.htm (815 words)

	PlanetMath: Kleene star
		The definition of Kleene star can be generalized so that it operates on any monoid
		See Also: alphabet, string, regular expression, Kleene algebra, language, convolution, weight (strings), weight enumerator
		This is version 2 of Kleene star, born on 2002-02-24, modified 2002-05-03.
	planetmath.org /encyclopedia/KleeneStar.html (146 words)

	Hypotheses in Kleene Algebra - Cohen (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		Abstract: Kleene algebra (an Horn axiomatization of Kleene's algebra of regular events) has proved to be an effective tool for reasoning about programs.
		Within the algebra, we can reason succinctly about both ordinary safety properties and important program transformations such as loop unwinding, change of data representation, and refinement of atomicity.
		One of the nice properties of Kleene algebra is that its equational theory has a simple decision procedure.
	citeseer.ist.psu.edu /1688.html (383 words)

	[No title]
		Kleene algebra: an idempotent semiring with additional unary operator (the Kleene star); these are modeled on
		Commutative algebra: an associative algebra whose multiplication is commutative
		Those statements that apply to all algebraic structures collectively are investigated in the branch of mathematics known as universal algebra.
	en-cyclopedia.com /wiki/Algebraic_structure (400 words)

	The Kleene Algebra of Nested Pointer Structures: Theory and Applications
		The framework is based on Kleene algebra, which despite its simple structure has been successfully applied to a variety of different problems.
		The algebra is used as formal basis for a transformation system to derive correct pointer algorithms from functional specifications.
		As a further application it is shown that pointer Kleene algebra can also serve as an algebraic model behind a Hoare-style verification system for algorithms on linked data structures.
	www.informatik.uni-augsburg.de /lehrstuehle/dbis/pmi/publications/dissertations/2003_ehm (325 words)

	IBFI Schloss Dagstuhl - Dagstuhl Seminar 01081 (Site not responding. Last check: 2007-10-20)
		It has also recently been observed that Kleene algebra provides a useful verification tool that can be used to establish basic program equivalences that arise in low-level verification tasks such as verification of communication protocols or compiler optimization.
		Dropping one of the distributivity requirements for Kleene algebras leads to a system that is close to process algebras such as ACP or μCRL.
		Compared with other algebraic approaches to semantics, such as relation algebra or sequential calculus, Kleene algebra and its relatives enjoy a particularly simple axiomatisation, since they do not use a notion of (pseudo)- converse and the corresponding axioms.
	www.dagstuhl.de /01081 (836 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-20)
		In abstract algebra, an algebraic structure consists of a set together with a collection of operations or relations defined on it which satisfy certain axioms.
		Kleene algebra: an idempotent semiring with additional unary operator (the Kleene star); these are modeled on regular expressions
		Clifford algebra: an associative algebra determined by quadratic form on a vector space
	www.alanaditescili.net /index.php?title=Algebraic_structure (519 words)

	ipedia.com: Kleene star Article (Site not responding. Last check: 2007-10-20)
		In mathematical logic and computer science, the Kleene star is a unary operation, either on sets of strings or on sets of symbols or characters.The application of the Kleene star to a set V is written...
		In mathematical logic and computer science, the Kleene star (or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters.The application of the Kleene star to a set V is written as V*.
		It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene (1909-1994) to characterise certain automata.
	www.ipedia.com /kleene_star.html (394 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		It arises in many contexts: relational algebra, semantics and logics of programs, automata and formal language theory, and the design and analysis of algorithms.
		A Kleene algebra with tests is a Kleene algebra with an embedded Boolean subalgebra.
		We illustrate the use of Kleene algebra with tests by giving a purely equational proof of the following classical result: every while program can be simulated by a while program with at most one while loop.
	www.diku.dk /topps/activities/topps-talks/1997/971027 (239 words)

	PlanetMath: Kleene algebra
		Regular expressions are a form (or close variant) of a Kleene algebra.
		Cross-references: regular expressions, satisfies, Kleene star, operator, unary, semiring, idempotent
		This is version 2 of Kleene algebra, born on 2002-02-24, modified 2002-05-03.
	planetmath.org /encyclopedia/KleeneAlgebra.html (77 words)

	RelMiCS 8
		Algebraic logic, in which the calculus of relations plays a prominent part, was taken up by Peirce, Schröder, and subsequently by Tarski in his seminal paper
		On the calculus of relations, in 1941; this gave rise to the study of relation algebras, which in its modern form overlaps with universal algebra, model theory, nonclassical logics, and category theory.
		The role of the calculus of relations in the interaction between algebra and logic is now well understood, and relational methods are part of the toolbox of the mathematician and logician.
	www.cosc.brocku.ca /Faculty/Winter/RelMiCS8 (621 words)

	DIMACS Workshop on Applications of Lattices and Ordered Sets to Computer Science
		Omega algebra - an extension of Kleene algebra to omega-regular expressions - has proved to be a useful tool, particularly for reasoning about concurrency control.
		Kozen's Kleene algebra with tests (KAT) extends this classical framework by an abstract representation of sets of states.
		The use of this predicate transformer algebra is exemplified in the derivation of some general formulations of greedy-like algorithms.
	dimacs.rutgers.edu /Workshops/Lattices/abstracts.html (3384 words)

	CATS Spring 1998 abstracts
		Parts I and II of this series concentrated on algebraic aspects of P-recursive sequences.
		In some cases, such as counting labled triangle-free cubic graphs, reduction can be applied when the more algebraic methods don't seem to work.
		Kleene algebras are algebraic structures with operators +,.
	www.cs.uga.edu /~rwr/Seminar/S98.html (861 words)

	On Hoare Logic and Kleene Algebra with Tests - Kozen (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		The goal of this paper is to develop a coalgebraic theory of KAT, paralleling the coalgebraic treatment of KA.
		9 Hypotheses in Kleene algebra - Cohen - 1994
		Parikh's Theorem in Commutative Kleene Algebra - Hopkins, Kozen (1999)
	citeseer.ist.psu.edu /kozen98hoare.html (655 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		A Coalgebraic Approach to Kleene Algebra with Tests Hubie Chen and Riccardo Pucella Kleene Algebra with Tests is an extension of Kleene Algebra, the algebra of regular expressions, allowing for boolean tests to be interspersed with program actions.
		We develop a coalgebraic theory of Kleene Algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata.
		Since the known automata-theoretic presentation of Kleene Algebra with Tests does not lend itself to a coalgebraic theory, we define a new interpretation of Kleene Algebra with Tests expressions and a corresponding automata-theoretic presentation, and impose a type system on expressions to guarantee that presentation.
	www.mathematik.uni-marburg.de /~cmcs/Abstracts/Chen.php (133 words)

	DBLP: Jules Desharnais (Site not responding. Last check: 2007-10-20)
		Jules Desharnais, Bernhard Möller, Georg Struth: Kleene algebra with domain.
		Jules Desharnais, Bernhard Möller, Georg Struth: Termination in Modal Kleene Algebra.
		Jules Desharnais, Bernhard Möller: Characterizing determinacy in Kleene algebras.
	www.informatik.uni-trier.de /~ley/db/indices/a-tree/d/Desharnais:Jules.html (665 words)

	Allegra Angus receives computer science award (Site not responding. Last check: 2007-10-20)
		Professor in Engineering, and deals with Kleene algebra, a method of working with what are called "regular expressions." Regular expressions are familiar to some computer users as a way of describing things that have a common overall pattern but differ in details.
		Angus has been working with an extension of Kleene algebra called Kleene algebra with tests (KAT), which allows a user to expand the use of regular expressions to describe computer programs and statements about those programs.
		Although she has spent her senior year concentrating on classes and research, Angus pursued her musical interests through most of her four years at Cornell, playing with the Cornell Symphony Orchestra and the Chamber Orchestra and singing in the women's chorus.
	www.news.cornell.edu /Chronicles/12.13.01/Angus.html (554 words)

	Articles - Algebraic structure (Site not responding. Last check: 2007-10-20)
		When there are no ambiguities, mathematicians usually identify the set with the algebraic structure.
		Algebraic structures are defined by the operations, relations and axioms that underlie them.
		Set: a set can itself be thought of as a degenerate algebraic structure, one that has zero operations defined on it
	lastring.com /articles/Algebraic_structure?... (611 words)

	Abstract Nr. 146 (Site not responding. Last check: 2007-10-20)
		We prove Church-Rosser statements in Kleene algebra in the spirit of the point-free style of functional programming.
		In the strip lemma of the $\lambda$-calculus, the term and algebra part are cleanly separated.
		Using allegoric techniques, we also prove algebraic variants of Newman's lemma and Church-Rosser statements modulo an equivalence relation, in which the well-foundedness assumptions are derived.
	www.informatik.uni-freiburg.de /tr/2001/Report146/.index_g.html (135 words)

	Many-valued Logics (Site not responding. Last check: 2007-10-20)
		De Morgan algebras, Kleene algebras, and Boolean algebras.
		Heyting algebras, double Heyting algebras, and symmetrical Heytings algebras.
		Non-distributive quasi-lattice as an algebra for fuzzy set theory of type 2.
	www.logic.ru /Engl/Books/ContLC4e.html (285 words)

	Historia Matematica Mailing List Archive by thread
		Re: [HM] The Fundamental Theorem of Algebra Renate Tobies
		Re: [HM] The Fundamental Theorem of Algebra Julio Gonzalez Cabillon
		Re: [HM] The Fundamental Theorem of Algebra Gerhard Warnecke
	sunsite.utk.edu /math_archives/.http/hypermail/historia/nov98 (1477 words)

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