On the Axiomatizability of Impossible Futures
Abstract
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.
Keywords
Cite
@article{arxiv.1505.04985,
title = {On the Axiomatizability of Impossible Futures},
author = {Taolue Chen and Wan Fokkink and Rob van Glabbeek},
journal= {arXiv preprint arXiv:1505.04985},
year = {2017}
}