# On the axiomatizability of impossible futures

## Authors

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