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195
Kleene Algebra with Converse
"... Abstract The equational theory generated by all algebras of binary relations with operations of union, composition, converse and reflexive transitive closure was studied by Bernátsky, Bloom, Ésik, and Stefanescu in 1995. We reformulate some of their proofs in syntactic and elementary terms, and we ..."
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Abstract The equational theory generated by all algebras of binary relations with operations of union, composition, converse and reflexive transitive closure was studied by Bernátsky, Bloom, Ésik, and Stefanescu in 1995. We reformulate some of their proofs in syntactic and elementary terms, and we
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
GreedyLike Algorithms in Modal Kleene Algebra
"... This study provides an algebraic background for the formal derivation of greedylike algorithms. We propose Kleene algebra as a particularly simple alternative to previous approaches such as relation algebra. Instead of converse and residuation we use modal operators that are definable in a wide c ..."
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Cited by 2 (2 self)
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This study provides an algebraic background for the formal derivation of greedylike algorithms. We propose Kleene algebra as a particularly simple alternative to previous approaches such as relation algebra. Instead of converse and residuation we use modal operators that are definable in a wide
On Kleene Algebras and Closed Semirings
, 1990
"... 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. The literature contains several inequivalent definitions of Kleene algebras and ..."
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Cited by 55 (6 self)
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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. The literature contains several inequivalent definitions of Kleene algebras
Simplifying Pointer Kleene Algebra
"... Pointer Kleene algebra has proved to be a useful abstraction for reasoning about reachability properties and correctly deriving pointer algorithms. Unfortunately it comes with a complex set of operations and defining (in)equations which exacerbates its practicability with automated theorem proving s ..."
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Cited by 1 (0 self)
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Pointer Kleene algebra has proved to be a useful abstraction for reasoning about reachability properties and correctly deriving pointer algorithms. Unfortunately it comes with a complex set of operations and defining (in)equations which exacerbates its practicability with automated theorem proving
A tactic for deciding Kleene algebras
 In 1st Coq Workshop. Tech. Univ
, 2009
"... We present a Coq reflexive tactic for deciding equalities or inequalities in Kleene algebras. This tactic is part of a larger project, whose aim is to provide tools for reasoning about binary relations in Coq: binary relations form a Kleene algebra, where the star operation is the reflexive transiti ..."
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Cited by 13 (3 self)
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We present a Coq reflexive tactic for deciding equalities or inequalities in Kleene algebras. This tactic is part of a larger project, whose aim is to provide tools for reasoning about binary relations in Coq: binary relations form a Kleene algebra, where the star operation is the reflexive
Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests
"... We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multiterminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by explo ..."
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Cited by 5 (0 self)
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by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest datastructure from Hopcroft and Karp’s standard algorithm. Then we consider Kleene algebra
Decision Algorithms for Kleene Algebra with Tests and Hoare Logic
, 2012
"... I would like to thank my supervisors, professors Nelma Moreira and Sabine Broda, for their guidance, support and dedication over the last months. I would also like to thank David Pereira for all the fruitful discussions on Kleene algebra and for his help with the OCaml language. My final acknowledgm ..."
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I would like to thank my supervisors, professors Nelma Moreira and Sabine Broda, for their guidance, support and dedication over the last months. I would also like to thank David Pereira for all the fruitful discussions on Kleene algebra and for his help with the OCaml language. My final
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 19 (5 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
Properties of Overwriting for Updates in Typed Kleene Algebras
, 2000
"... In this paper we present an abstract representation of pointer structures in Kleene algebras and the properties of a particular selective update function. These can be used as prerequisites for the definition of insitu pointer updates and a general framework to derive insitu pointer algorithms f ..."
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Cited by 1 (1 self)
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In this paper we present an abstract representation of pointer structures in Kleene algebras and the properties of a particular selective update function. These can be used as prerequisites for the definition of insitu pointer updates and a general framework to derive insitu pointer algorithms
Results 1  10
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195