# Algebraic formulations of trace theory

## Abstract

In this paper mathematical models are given for Trace Theory as described in [Rem85] and [Kal86]. They model a process by a trace structure: a pair consisting of an alphabet and a trace set over this alphabet. We show that in fact two incompatible process models are used, and we devise a new model that has all essential characteristics of the two former models. A complete axiomatization of this model is given. It is shown that a distinction between successful and unsuccessful termination is needed to effectuate associativity of parallel composition with communication in the presence of sequential composition. Two operators generating infinite processes are added, which makes a verification of the alternating bit protocol possible.

## Key words and phrases

concurrency process algebra trace models complete axiomatization infinite processes verification alternating bit protocol## Preview

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## References

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