# On finite alphabets and infinite bases

Chen, Taolue and Fokkink, Wan and Luttik, Bas and Nain, Sumit
(2008)
*On finite alphabets and infinite bases.*
Information and Computation, 206
(5).
pp. 492-519.
ISSN 0890-5401

Full text is not in this repository.

## Abstract

Van Glabbeek presented the linear time–branching time spectrum of behavioral semantics. He studied these semantics in the setting of the basic process algebra BCCSP, and gave finite, sound and ground-complete, axiomatizations for most of these semantics. Groote proved for some of van Glabbeek’s axiomatizations that they are ω-complete, meaning that an equation can be derived if (and only if) all of its closed instantiations can be derived. In this paper, we settle the remaining open questions for all the semantics in the linear time–branching time spectrum, either positively by giving a finite sound and ground-complete axiomatization that is ω-complete, or negatively by proving that such a finite basis for the equational theory does not exist. We prove that in case of a finite alphabet with at least two actions, failure semantics affords a finite basis, while for ready simulation, completed simulation, simulation, possible worlds, ready trace, failure trace and ready semantics, such a finite basis does not exist. Completed simulation semantics also lacks a finite basis in case of an infinite alphabet of actions.

Item Type: | Article |
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Keywords (uncontrolled): | Concurrency; Process algebra; Equational theory; ω-completeness |

Research Areas: | A. > School of Science and Technology > Computer Science A. > School of Science and Technology > Computer Science > Foundations of Computing group |

Item ID: | 12075 |

Depositing User: | Users 3197 not found. |

Date Deposited: | 27 Sep 2013 08:47 |

Last Modified: | 26 Apr 2018 18:56 |

URI: | http://eprints.mdx.ac.uk/id/eprint/12075 |

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