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A completeness theorem for Kleene algebras and the algebra of regular events
 Information and Computation
, 1994
"... We givea nitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1 ..."
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Cited by 242 (27 self)
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We givea nitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1
Departamento de Ciência de Computadores
, 2014
"... This paper gives a new presentation of Kozen’s proof of Kleene algebra completeness featured in his article A completeness theorem for Kleene algebras and the algebra of regular events. A few new variants are introduced, shortening the proof. Specifically, we directly construct an εfree automaton t ..."
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This paper gives a new presentation of Kozen’s proof of Kleene algebra completeness featured in his article A completeness theorem for Kleene algebras and the algebra of regular events. A few new variants are introduced, shortening the proof. Specifically, we directly construct an εfree automaton
Kleene Algebra with Domain
, 2003
"... We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We ..."
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Cited by 53 (32 self)
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We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems
Hypotheses in Kleene Algebra
, 1994
"... 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 ..."
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Cited by 17 (2 self)
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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
Synchronous Kleene Algebra vs. Concurrent Kleene Algebra
"... Abstract. In this year’s CONCUR conference Concurrent Kleene Algebra (CKA) is presented as a general formalism for reasoning about concurrent programs. Also recently Synchronous Kleene Algebra (SKA) was investigated by this author with the purpose of representing and reasoning about actions/program ..."
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Abstract. In this year’s CONCUR conference Concurrent Kleene Algebra (CKA) is presented as a general formalism for reasoning about concurrent programs. Also recently Synchronous Kleene Algebra (SKA) was investigated by this author with the purpose of representing and reasoning about actions
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 10 (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
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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] and Salgebras [2] are strongly related by adjunctions. The axioms of Kleene algebra in the sense of [6] are not complete for the universal Horn theory of the regular events. This refutes a conjecture of Conway [2, p. 103]. Righthanded Kleene algebras are not necessarily lefthanded Kleene algebras
Foundations of Concurrent Kleene Algebra
"... A Concurrent Kleene Algebra offers two composition operators, one that stands for sequential execution and the other for concurrent execution [10]. In this paper we investigate the abstract background of this law in terms of independence relations on which a concrete trace model of the algebra is b ..."
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Cited by 5 (2 self)
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A Concurrent Kleene Algebra offers two composition operators, one that stands for sequential execution and the other for concurrent execution [10]. In this paper we investigate the abstract background of this law in terms of independence relations on which a concrete trace model of the algebra
DECIDING KLEENE ALGEBRAS IN COQ
, 2011
"... braries to assist in the mechanization of formal proofs in Coq. The first library provides algebraic tools for reasoning about binary relations and can be found at ..."
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braries to assist in the mechanization of formal proofs in Coq. The first library provides algebraic tools for reasoning about binary relations and can be found at
Lazy Caching in Kleene Algebra
, 1994
"... We use Kleene algebra to give a proof of the lazy caching protocol of Afek, Brown and Merritt. The proof is reasonably concise, but its steps can be checked by (mechanizable) straightline program reasoning. 1 Introduction Distributed system design is a notoriously errorprone activity. For this re ..."
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Cited by 7 (0 self)
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We use Kleene algebra to give a proof of the lazy caching protocol of Afek, Brown and Merritt. The proof is reasonably concise, but its steps can be checked by (mechanizable) straightline program reasoning. 1 Introduction Distributed system design is a notoriously errorprone activity
Results 1  10
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175,307