Chen, Taolue and Fokkink, Wan and van Glabbeek, Rob - On the Axiomatizability of Impossible Futures

lmcs:1593 - Logical Methods in Computer Science, September 22, 2015, Volume 11, Issue 3
On the Axiomatizability of Impossible Futures

Authors: Chen, Taolue and Fokkink, Wan and van Glabbeek, Rob

A general method is established to derive a ground-complete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves omega-completeness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, ground- and omega-complete axiomatizations are derived for weak failures, completed trace and trace semantics. We then present a finite, sound, ground-complete axiomatization for the concrete impossible futures preorder, which implies a finite, sound, ground-complete axiomatization for the weak impossible futures preorder. In contrast, we prove that no finite, sound axiomatization for BCCS modulo concrete and weak impossible futures equivalence is ground-complete. If the alphabet of actions is infinite, then the aforementioned ground-complete axiomatizations are shown to be omega-complete. If the alphabet is finite, we prove that the inequational theories of BCCS modulo the concrete and weak impossible futures preorder lack such a finite basis.


Source : oai:arXiv.org:1505.04985
DOI : 10.2168/LMCS-11(3:17)2015
Volume: Volume 11, Issue 3
Published on: September 22, 2015
Submitted on: January 4, 2015
Keywords: Computer Science - Logic in Computer Science


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