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Kleene algebra with tests
 Transactions on Programming Languages and Systems
, 1997
"... Abstract. We investigate conditions under which a given Kleene algebra with tests is isomorphic to an algebra of binary relations. Two simple separation properties are identified that, along with starcontinuity, are sufficient for nonstandard relational representation. An algebraic condition is ide ..."
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Cited by 145 (28 self)
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Abstract. We investigate conditions under which a given Kleene algebra with tests is isomorphic to an algebra of binary relations. Two simple separation properties are identified that, along with starcontinuity, are sufficient for nonstandard relational representation. An algebraic condition
Complexity of Kleene Algebra with Tests
, 2004
"... In this lecture we show that the equational theory of KAT is PSPACEcomplete. Thus KAT, while considerably more expressive than KA without tests, is no more difficult to decide. ..."
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In this lecture we show that the equational theory of KAT is PSPACEcomplete. Thus KAT, while considerably more expressive than KA without tests, is no more difficult to decide.
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
Kleene Algebras and Pointer Structures
, 2003
"... Kleene algebras (KA) have turned out to be an appropriate tool to formally describe algebraic systems in various areas. Despite this universal applicability there often proofs are easy and half as long as in concrete KAs. In this paper we describe how to use KAs to model edgelabeled directed graphs ..."
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Cited by 1 (1 self)
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Kleene algebras (KA) have turned out to be an appropriate tool to formally describe algebraic systems in various areas. Despite this universal applicability there often proofs are easy and half as long as in concrete KAs. In this paper we describe how to use KAs to model edgelabeled directed
Deciding Kleene Algebras in Coq
 Logical Methods in Computer Science
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 4 (0 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
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
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
On Hoare Logic and Kleene Algebra with Tests
"... We show that Kleene algebra with tests (KAT) subsumes propositional Hoare logic (PHL). Thus the specialized syntax and deductive apparatus of Hoare logic are inessential and can be replaced by simple equational reasoning. In addition, we show that all relationally valid inference rules are derivable ..."
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Cited by 56 (13 self)
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We show that Kleene algebra with tests (KAT) subsumes propositional Hoare logic (PHL). Thus the specialized syntax and deductive apparatus of Hoare logic are inessential and can be replaced by simple equational reasoning. In addition, we show that all relationally valid inference rules
Automatic Proof Generation in Kleene Algebra with Tests
, 2007
"... Kleene algebra (KA) is the algebra of regular events. Familiar examples of Kleene algebras include regular sets, relational algebras, and trace algebras. A Kleene algebra with tests (KAT) is a Kleene algebra with an embedded Boolean subalgebra. The addition of tests allows one to encode while progra ..."
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Kleene algebra (KA) is the algebra of regular events. Familiar examples of Kleene algebras include regular sets, relational algebras, and trace algebras. A Kleene algebra with tests (KAT) is a Kleene algebra with an embedded Boolean subalgebra. The addition of tests allows one to encode while
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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acknowledgments go to my family for their continuous support. 3 Kleene algebra with tests (KAT) is an equational system for program verification, which is the combination of Boolean algebra (BA) and Kleene algebra (KA), the algebra of regular expressions. In particular, KAT subsumes the propositional fragment
Results 1  10
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158,334