Abstract
This paper studies the existence of finite equational axiomatisations of the interleaving parallel composition operator modulo the behavioural equivalences in van Glabbeek's linear time-branching time spectrum. In the setting of the process algebra BCCSP over a finite set of actions, we provide finite, ground-complete axiomatisations for various simulation and (decorated) trace semantics. We also show that no congruence over BCCSP that includes bisimilarity and is included in possible futures equivalence has a finite, ground-complete axiomatisation; this negative result applies to all the nested trace and nested simulation semantics.
Highlights
Process algebras [BPS01, BBR10] are prototype specification languages allowing for the description and analysis of concurrent and distributed systems, or processes
We consider the process algebra BCCSP, i.e., BCCSP enriched with the interleaving parallel composition operator, and we study the existence of finite equational axiomatisations of the behavioural congruences in the linear time-branching time spectrum over it
We have studied the finite axiomatisability of the language BCCSP modulo the behavioural equivalences in the linear time-branching time spectrum
Summary
Process algebras [BPS01, BBR10] are prototype specification languages allowing for the description and analysis of concurrent and distributed systems, or processes. These languages offer a variety of operators to specify composite processes from components one has already built. Behavioural equivalences have been introduced, in the second step, as simple and elegant tools for comparing the behaviour of processes. These are equivalence relations defined on the states of LTSs allowing one to establish whether two processes have the same observable behaviour.
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