Abstract

Pomsets have been introduced as a mode2 of concurrency. Since a pomset is a string in which the total order has been relaxed to be a partial order, in this paper we view them as a generalization cf Strings, and investigate their algebraic properties. In particular, we investigate the axiomatic properties of pornsets, sets of pomsets and ideals of pornsets, under such operations as concatenation, parallel composition, union and their associated closure operations. We find that the equational theory of sets, pomsets under concatenation, parallel composition and union is finitely axiomatizable, whereas the theory of languages under the analogous operations is not. A similar result is obtained for ideals of pornsets, which incorporate the notion of subsumption which is also known as auaentation. Finally, we show that the addition of any closure operation (parallel or serial) Ieads to nonfinite axiomatizability of the resulting equational theory.

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