Kleene Algebra with Tests: Completeness and Decidability (1996)
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| Venue: | Proc. 10th Int. Workshop Computer Science Logic (CSL'96), volume 1258 of Lecture Notes in Computer Science |
| Citations: | 19 - 9 self |
BibTeX
@INPROCEEDINGS{Kozen96kleenealgebra,
author = {Dexter Kozen and Frederick Smith},
title = {Kleene Algebra with Tests: Completeness and Decidability},
booktitle = {Proc. 10th Int. Workshop Computer Science Logic (CSL'96), volume 1258 of Lecture Notes in Computer Science},
year = {1996},
pages = {244--259},
publisher = {Springer-Verlag}
}
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Abstract
. Kleene algebras with tests provide a rigorous framework for equational specification and verification. They have been used successfully in basic safety analysis, source-to-source program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra with tests and *-continuous Kleene algebra with tests over language-theoretic and relational models. We also show decidability. Cohen's reduction of Kleene algebra with hypotheses of the form r = 0 to Kleene algebra without hypotheses is simplified and extended to handle Kleene algebras with tests. 1 Introduction A Kleene algebra with tests is an algebraic structure consisting of a Kleene algebra with an embedded Boolean subalgebra. This formalism provides a rigorous framework for equational specification and verification of programs. It has been applied successfully to problems in basic safety analysis, source-to-source program transformation, and concurrency control [3, 4, 5, 17]. Kleene ...
