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Automated reasoning in Kleene algebra
 CADE 2007, LNCS 4603
, 2007
"... Abstract. It has often been claimed that model checking, special purpose automated deduction or interactive theorem proving are needed for formal program development. We demonstrate that offtheshelf automated proof and counterexample search is an interesting alternative if combined with the right ..."
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Cited by 21 (11 self)
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Abstract. It has often been claimed that model checking, special purpose automated deduction or interactive theorem proving are needed for formal program development. We demonstrate that offtheshelf automated proof and counterexample search is an interesting alternative if combined with the right domain model. We implement variants of Kleene algebras axiomatically in Prover9/Mace4 and perform proof experiments about Hoare, dynamic, temporal logics, concurrency control and termination analysis. They confirm that a simple automated analysis of some important program properties is possible. Particular benefits of this novel approach include “soft ” model checking in a firstorder setting, crosstheory reasoning between standard formalisms and full automation of some (co)inductive arguments. Kleene algebras might therefore provide lightweight formal methods with heavyweight automation. 1
Modal Kleene Algebra And Applications  A Survey
, 2004
"... Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey ..."
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Cited by 11 (5 self)
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Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey
KATML: An interactive theorem prover for Kleene Algebra with Tests
 University of Manchester
, 2003
"... Abstract. We describe an implementation of an interactive theorem prover for Kleene algebra with tests (KAT). The system is designed to reflect the natural style of reasoning with KAT that one finds in the literature. We illustrate its use with some examples. 1 ..."
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Cited by 11 (1 self)
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Abstract. We describe an implementation of an interactive theorem prover for Kleene algebra with tests (KAT). The system is designed to reflect the natural style of reasoning with KAT that one finds in the literature. We illustrate its use with some examples. 1
Termination in Modal Kleene Algebra
 EXPLORING NEW FRONTIERS OF THEORETICAL INFORMATICS. IFIP INTERNATIONAL FEDERATION FOR INFORMATION PROCESSING SERIES 155. KLUWER 2004, 653–666
, 2004
"... Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspond ..."
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Cited by 9 (8 self)
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Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspondence proof of Lob's formula from modal logic. It gives calculational proofs of two fundamental statements from rewriting theory that involve termination: Bachmair's and Dershowitz's wellfounded union theorem and Newman's lemma. These results are also of general interest for the termination analysis of programs and state transition systems.
An Efficient Coq Tactic for Deciding Kleene Algebras
, 2009
"... We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations almost instantaneously. The corresponding decision procedure was ..."
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Cited by 9 (2 self)
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We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations almost instantaneously. The corresponding decision procedure was proved correct and complete; correctness is established w.r.t. any model (including binary relations), by formalising Kozen’s initiality theorem.
A PROOFTHEORETIC APPROACH TO MATHEMATICAL KNOWLEDGE MANAGEMENT
, 2007
"... Mathematics is an area of research that is forever growing. Definitions, theorems, axioms, and proofs are integral part of every area of mathematics. The relationships between these elements bring to light the elegant abstractions that bind even the most intricate aspects of math and science. As the ..."
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Cited by 7 (0 self)
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Mathematics is an area of research that is forever growing. Definitions, theorems, axioms, and proofs are integral part of every area of mathematics. The relationships between these elements bring to light the elegant abstractions that bind even the most intricate aspects of math and science. As the body of mathematics becomes larger and its relationships become richer, the organization of mathematical knowledge becomes more important and more difficult. This emerging area of research is referred to as mathematical knowledge management (MKM). The primary issues facing MKM were summarized by Buchberger, one of the organizers of the first Mathematical Knowledge Management Workshop [20]. • How do we retrieve mathematical knowledge from existing and future sources? • How do we build future mathematical knowledge bases? • How do we make the mathematical knowledge bases available to mathematicians? These questions have become particularly relevant with the growing power of and interest in automated theorem proving, using computer programs to prove
Greedylike algorithms in Kleene algebra
 PARTICIPANTS’ PROCEEDINGS 7TH RELMICS/2ND KLEENE WORKSHOP, MALENTE, MAY 12–17, 2003
, 2003
"... This paper provides an algebraic background for the formal derivation of greedylike algorithms. Such derivations have previously been done in various frameworks including relation algebra. We propose Kleene algebra as a particularly simple alternative. Instead of converse and residuation we use mo ..."
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Cited by 2 (2 self)
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This paper provides an algebraic background for the formal derivation of greedylike algorithms. Such derivations have previously been done in various frameworks including relation algebra. We propose Kleene algebra as a particularly simple alternative. Instead of converse and residuation we use modal operators that are definable in a wide class of algebras, based on domain/codomain or image/preimage operations. By abstracting from earlier approaches we arrive at a very general theorem about the correctness of loops that covers particular forms of greedy algorithms as special cases.
devant le jury composé de:
, 2006
"... dans l’école doctorale de Mathématiques, Sciences et Technologies de ..."
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