# On the axiomatizability of impossible futures

## Authors

Rob van Glabbeek, Taolue Chen and Wan Fokkink

NICTA

UNSW

Middlesex University

London

VU University

Amsterdam

## 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.

## BibTeX Entry

@article{vanGlabbeek_CF_15,
doi = {10.2168/LMCS-11(3:17)2015},
month = sep,
paperurl = {https://trustworthy.systems/publications/nicta_full_text/8502.pdf},
journal = {Logical Methods in Computer Science},
year = {2015},
keywords = {concurrency, process algebra, bccs, labeled transition systems, complete axiomatizations, impossible
futures semantics.},
volume = {11},
title = {On the Axiomatizability of Impossible Futures},
number = {3},
author = {van Glabbeek, Robert and Chen, Taolue and Fokkink, Wan},
pages = {1--31}
}

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