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On the Completeness of the Equations for the Kleene Star in Bisimulation (1996)
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| Venue: | In Proceedings AMAST'96, LNCS 1101 |
| Citations: | 9 - 3 self |
BibTeX
@INPROCEEDINGS{Fokkink96onthe,
author = {Wan Fokkink},
title = {On the Completeness of the Equations for the Kleene Star in Bisimulation},
booktitle = {In Proceedings AMAST'96, LNCS 1101},
year = {1996},
pages = {180--194},
publisher = {Springer}
}
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Abstract
. A classical result from Redko [20] says that there does not exist a complete finite equational axiomatization for the Kleene star modulo trace equivalence. Fokkink and Zantema [13] showed, by means of a term rewriting analysis, that there does exist a complete finite equational axiomatization for the Kleene star up to strong bisimulation equivalence. This paper presents a simpler and shorter completeness proof. Furthermore, the result is extended to open terms, i.e., to !-completeness. Finally, it is shown that the three equations for the Kleene star are all essential for completeness. 1 Introduction Kleene [15] defined a binary operator x y in the context of finite automata, which denotes the iterate of x on y. Intuitively, the expression x y can choose to execute either x, after which it evolves into x y again, or y, after which it terminates. An advantage of the Kleene star is that on the one hand it can express recursion, while on the other hand it can be captured in eq...
