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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 152 (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
Kleene algebra with tests: Completeness and decidability
 IN PROC. OF 10TH INTERNATIONAL WORKSHOP ON COMPUTER SCIENCE LOGIC (CSL’96
, 1996
"... Kleene algebras with tests provide a rigorous framework for equational specification and verification. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra w ..."
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Cited by 37 (15 self)
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Kleene algebras with tests provide a rigorous framework for equational specification and verification. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra
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 60 (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
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 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
On the coalgebraic theory of Kleene algebra with tests
, 2008
"... We develop a coalgebraic theory of Kleene algebra with tests (KAT) along the lines of Rutten (1998) for Kleene algebra (KA) and Chen and Pucella (2003) for a limited version of KAT, resolving some technical issues raised by Chen and Pucella. Our treatment includes a simple definition of the Brzozows ..."
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Cited by 27 (2 self)
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We develop a coalgebraic theory of Kleene algebra with tests (KAT) along the lines of Rutten (1998) for Kleene algebra (KA) and Chen and Pucella (2003) for a limited version of KAT, resolving some technical issues raised by Chen and Pucella. Our treatment includes a simple definition
An axiomatization of arrays for Kleene algebra with tests
 In: Proc. 9th Int. Conf. Relational Methods in Computer Scienceand 4th Int. Workshop Applications of Kleene Algebra (RelMiCS/AKA’06). Volume 4136 of LNCS
, 2006
"... Abstract. The formal analysis of programs with arrays is a notoriously difficult problem due largely to aliasing considerations. In this paper we augment the rules of Kleene algebra with tests (KAT) with rules for the equational manipulation of arrays in the style of schematic KAT. These rules captu ..."
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Cited by 1 (0 self)
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Abstract. The formal analysis of programs with arrays is a notoriously difficult problem due largely to aliasing considerations. In this paper we augment the rules of Kleene algebra with tests (KAT) with rules for the equational manipulation of arrays in the style of schematic KAT. These rules
Kleene algebra with tests and program schematology
, 2001
"... The theory of flowchart schemes has a rich history going back to Ianov [6]; see Manna [22] for an elementary exposition. A central question in the theory of program schemes is scheme equivalence. Manna presents several examples of equivalence proofs that work by simplifying the schemes using various ..."
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Cited by 22 (8 self)
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various combinatorial transformation rules. In this paper we present a purely algebraic approach to this problem using Kleene algebra with tests (KAT). Instead of transforming schemes directly using combinatorial graph manipulation, we regard them as a certain kind of automaton on abstract traces. We
On the elimination of hypotheses in Kleene algebra with tests
, 2002
"... The validity problem for certain universal Horn formulas of Kleene algebra with tests (KAT) can be efficiently reduced to the equational theory. This reduction is known as elimination of hypotheses. Hypotheses are used to describe the interaction of atomic programs and tests and are an essential com ..."
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Cited by 11 (5 self)
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The validity problem for certain universal Horn formulas of Kleene algebra with tests (KAT) can be efficiently reduced to the equational theory. This reduction is known as elimination of hypotheses. Hypotheses are used to describe the interaction of atomic programs and tests and are an essential
A Coalgebraic Approach to Kleene Algebra with Tests
 In volume 82(1) of ENTCS
, 2003
"... Kleene Algebra with Tests is an extension of Kleene Algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene Algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. ..."
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Cited by 7 (0 self)
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Kleene Algebra with Tests is an extension of Kleene Algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene Algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata
Results 1  10
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