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On the axiomatisability of priority

Published online by Cambridge University Press:  01 February 2008

LUCA ACETO ,
TAOLUE CHEN ,
WAN FOKKINK  and
ANNA INGOLFSDOTTIR
LUCA ACETO
Affiliation:
Reykjavík University, Department of Computer Science, Kringlan 1, 103 Reykjavík, Iceland Email: luca@ru.is, annai@ru.is
TAOLUE CHEN
Affiliation:
CWI, Embedded Systems Group, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
WAN FOKKINK
Affiliation:
CWI, Embedded Systems Group, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands Vrije Universiteit, Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
ANNA INGOLFSDOTTIR
Affiliation:
Reykjavík University, Department of Computer Science, Kringlan 1, 103 Reykjavík, Iceland Email: luca@ru.is, annai@ru.is
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Abstract

This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. We prove that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatisation over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatisations using equations with action predicates as conditions. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatisation consisting of equations with action predicates as conditions over the language studied in this paper. Finally, sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatisation of bisimulation equivalence using equations with action predicates as conditions.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Special Issue 1: in memory of Sauro Tulipani , February 2008 , pp. 5 - 28
Copyright
Copyright © Cambridge University Press2008

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