NDLI: Decision algoritms for Kleene algebra with tests and Hoare logic

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Decision algoritms for Kleene algebra with tests and Hoare logic

Content Provider	Semantic Scholar
Author	Almeida, Ricardo Manuel De Oliveira
Copyright Year	2012
Abstract	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 are very few software applications that implement KAT’s equational theory and/or provide adequate decision procedures. In this dissertation we present a new decision procedure for the equivalence of two KAT expressions based on the notion of partial derivatives. We provide some examples of proving the equivalence of two distinct programs using the procedure defined. We also introduce the notion of derivative modulo particular sets of equations. With this we extend the previous procedure for deciding PHL. We present some experimental results, including the proof of correction and the proof of safety of a program.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://sigarra.up.pt/icbas/pt/pub_geral.show_file?pi_gdoc_id=61610
Alternate Webpage(s)	http://www.dcc.fc.up.pt/~nam/web/resources/docs/thesisRA.pdf
Alternate Webpage(s)	https://repositorio-aberto.up.pt/bitstream/10216/65208/2/11725.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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