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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
On partially additive Kleene algebras
 In Proc. 8th Int. Conf. Relational Methods in Computer Science (RelMiCS 8
, 2005
"... We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras. We relate partially additive Kleene algebras to existing al ..."
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Cited by 2 (0 self)
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We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras. We relate partially additive Kleene algebras to existing
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
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
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
Kleene Algebra with Tests
, 2004
"... In semantics and logics of programs, Kleene algebra forms an essential component of Propositional Dynamic Logic (PDL) [6], in which it is mixed with Boolean algebra and modal logic ..."
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In semantics and logics of programs, Kleene algebra forms an essential component of Propositional Dynamic Logic (PDL) [6], in which it is mixed with Boolean algebra and modal logic
Modal Kleene Algebra and Partial Correctness
 INSTITUT FÜR INFORMATIK, UNIVERSITÄT AUGSBURG
, 2003
"... We enrich Kleene algebra by domain and codomain operators. These ..."
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Cited by 7 (7 self)
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We enrich Kleene algebra by domain and codomain operators. These
Typed Kleene algebra
, 1998
"... In previous work we havefound it necessary to argue that certain theorems of Kleene algebra hold even when the symbols are interpreted as nonsquare matrices. In this note we de ne and investigate typed Kleene algebra, a typed version of Kleene algebra in which objects have types s! t. Although nonsq ..."
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Cited by 23 (4 self)
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In previous work we havefound it necessary to argue that certain theorems of Kleene algebra hold even when the symbols are interpreted as nonsquare matrices. In this note we de ne and investigate typed Kleene algebra, a typed version of Kleene algebra in which objects have types s! t. Although
Characterizing Determinacy in Kleene Algebras
 INFORMATION SCIENCES
, 2000
"... Elements of Kleene algebras can be used, among others, as abstractions of the inputoutput semantics of nondeterministic programs or as models for the association of pointers with their target objects. In the first case, one seeks to distinguish the subclass of elements that correspond to determinist ..."
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Cited by 12 (5 self)
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Elements of Kleene algebras can be used, among others, as abstractions of the inputoutput semantics of nondeterministic programs or as models for the association of pointers with their target objects. In the first case, one seeks to distinguish the subclass of elements that correspond
Residuated Kleene Algebras
"... Abstract. We show that there is no finitely axiomatizable class of algebras that would serve as an analogue to Kozen’s class of Kleene algebras if we include the residuals of composition in the similarity type of relation algebras. 1 ..."
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Abstract. We show that there is no finitely axiomatizable class of algebras that would serve as an analogue to Kozen’s class of Kleene algebras if we include the residuals of composition in the similarity type of relation algebras. 1
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