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Step bisimulation is pomset equivalence on a parallel language without explicit internal choice

Published online by Cambridge University Press:  04 March 2009

Douglas R. Troeger
Douglas R. Troeger
Affiliation:
Department of Computer Sciences, The City College of New York, Convent Avenue at 138th Street, New York, NY 10031
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Abstract

We focus attention on a language ℒ generated by a set of elementary actions under operations of sequential composition, external binary choice, iteration, and non-nested disjoint parallel composition: that is, on an especially simple parallel language without explicit internal, or ‘local’, nondeterminism. ℒ is nondeterministic, despite the restriction to external choice, since a given action may occur in both subterms F and G of the parallel composition F ║ G. We exhibit a single set of equations that axiomatizes both step bisimulation and pomset equivalence on ℒ Given that step bisimulation and pomset equivalence are incomparable on the language ℒ+ obtained from ℒ by relaxing just the constraint on choice, the coincidence of these equivalences on ℒ suggests that the elimination of explicit internal choice can result in simplifications at the semantic level. We reinforce this impression by showing for ℒ that step bisimulation (i) coincides with pomset bisimulation equivalence, (ii) is real-time consistent, and (iii) has step trees as concrete representatives of its equivalence classes. Moreover, we show that none of these results holds for the language ℒ+ Finally, step trace equivalence is proved not to coincide with step bisimulation equivalence on ℒ.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 3 , Issue 1 , March 1993 , pp. 25 - 62
Copyright
Copyright © Cambridge University Press 1993

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