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2 KAT and Hoare Logic with Derivatives ∗
, 2013
"... 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 of Hoare logic (PHL) which is a formal system for the ..."
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Cited by 3 (2 self)
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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 of Hoare logic (PHL) which is a formal system for the specification and verification of programs, and that is currently the base of most tools for checking program correctness. Both the equational theory of KAT and the encoding of PHL in KAT are known to be decidable. In this paper we present a new decision procedure for the equivalence of two KAT expressions based on the notion of partial derivatives. We also introduce the notion of derivative modulo particular sets of equations. With this we extend the previous procedure for deciding PHL. Some experimental results are also presented. 1
Manipulation of Extended Regular Expressions with Derivatives∗
, 2013
"... The use of derivatives for efficiently deciding equivalence and membership in regular languages has been a major topic of recent research. To ensure termination, regular expressions must be considered modulo some algebraic properties such as associativity, commutativity, and idempotence of union (AC ..."
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The use of derivatives for efficiently deciding equivalence and membership in regular languages has been a major topic of recent research. To ensure termination, regular expressions must be considered modulo some algebraic properties such as associativity, commutativity, and idempotence of union (ACI). In this paper we describe an implementation of regular expressions modulo ACI and several derivative based methods within the FAdo system. Although regular languages are trivially closed for boolean operations, the manipulation of intersection and complementation with regular expressions or nondeterministic finite automata is non trivial and leads to an exponential blow up. However, due to several applications where extended regular expressions (XRE) are used to represent information, it is important the extension of derivative based methods to those operations. Continuing work of Caron et al., we present new algorithms for computing the (extended) equation automaton and deciding membership and equivalence of XRE using (partial) derivatives. 1 Extended Regular Expressions and Kleene Algebra
Departamento de Ciência de Computadores,
"... 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 of Hoare logic (PHL) which is a formal system for th ..."
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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 of Hoare logic (PHL) which is a formal system for the specification and verification of programs, and that is currently the base of most tools for checking program correctness. Both the equational theory of KAT and the encoding of PHL in KAT are known to be decidable. In this paper we present a new decision procedure for the equivalence of two KAT expressions based on the notion of partial derivatives. We also introduce the notion of derivative modulo particular sets of equations. With this we extend the previous procedure for deciding PHL. Some experimental results are also presented. 1
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 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 of Hoare logic (PHL) which is a formal system for the specification and verification of programs, and that is currently the base of most tools for checking program correctness. Both the equational theory of KAT and the encoding of PHL in KAT are known to be decidable. In spite of KAT’s success in dealing with several software verification tasks, there