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Some Remarks on Weak Bisimilarity of BPA-Processes

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Original title:Some Remarks on Weak Bisimilarity of BPA-Processes
Authors:Ivana Černá, Jitka Stříbrná
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Original language:English
Field:Information theory
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The purpose of this work is to examine the decidability problem of weak bisimilarity for BPA-processes. It has been known that strong bisimilarity, which may be considered a special case of weak bisimilarity, where the internal (silent) action tau is treated equally to observable actions, is decidable for BPA-processes. For strong bisimilarity, these processes are finitely branching and so for two non-bisimilar processes there exists a level n that distinguishes the two processes. Additionally, from the decidability of whether two processes are equivalent at a given level n, semidecidability of strong non-bisimilarity directly follows. We examine the following two closely related approaches to semidecidability of strong equivalence: of a (finite) bisimulation or expansion tree, of a finite Caucal base. We have attempted to find out if any of the above mentioned approaches could be generalized to (semi)decide weak bisimilarity. Our findings indicate that a direct generalization is not sufficient and an efficient (semi)decision procedure cannot be obtained in this way.

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