### Abstract

Original language | English |
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Journal | Logical Methods in Computer Science |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 |

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*Logical Methods in Computer Science*,

*11*(3). https://doi.org/10.2168/LMCS-11(3:17)2015

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*Logical Methods in Computer Science*, vol. 11, no. 3. https://doi.org/10.2168/LMCS-11(3:17)2015

**On the axiomatizability of impossible futures.** / Chen, T.; Fokkink, W.J.; van Glabbeek, R.J.

Research output: Contribution to Journal › Article › Academic › peer-review

TY - JOUR

T1 - On the axiomatizability of impossible futures

AU - Chen, T.

AU - Fokkink, W.J.

AU - van Glabbeek, R.J.

PY - 2015

Y1 - 2015

N2 - 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 ω completeness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, ground- and ω complete axiomatizations are derived for weak failures, completed trace and trace semantics. We then present a ω nite, sound, ground-complete axiomatization for the concrete impossible futures preorder, which implies a ω nite, sound, ground-complete axiomatization for the weak impossible futures preorder. In contrast, we prove that no ω nite, sound axiomatization for BCCS modulo concrete and weak impossible futures equivalence is ground-complete. If the alphabet of actions is in_nite, then the aforementioned ground- complete axiomatizations are shown to be ω complete. If the alphabet is ω nite, we prove that the inequational theories of BCCS modulo the concrete and weak impossible futures preorder lack such a ω nite basis.

AB - 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 ω completeness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, ground- and ω complete axiomatizations are derived for weak failures, completed trace and trace semantics. We then present a ω nite, sound, ground-complete axiomatization for the concrete impossible futures preorder, which implies a ω nite, sound, ground-complete axiomatization for the weak impossible futures preorder. In contrast, we prove that no ω nite, sound axiomatization for BCCS modulo concrete and weak impossible futures equivalence is ground-complete. If the alphabet of actions is in_nite, then the aforementioned ground- complete axiomatizations are shown to be ω complete. If the alphabet is ω nite, we prove that the inequational theories of BCCS modulo the concrete and weak impossible futures preorder lack such a ω nite basis.

U2 - 10.2168/LMCS-11(3:17)2015

DO - 10.2168/LMCS-11(3:17)2015

M3 - Article

VL - 11

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

IS - 3

ER -