A Calculus of Incomplete Fusions

Parrow and Victor introduced the fusion calculus (FC) (IEEE Symposium on Logic in Computer Science 1998) as a canonically reduced calculus of concurrency. In this paper, we consider an extension to the FC to deal with possible effects of non-Byzantine errors in name fusions. Extended syntax is defined in terms of meta-names and probabilistic variant of matching conditions with corresponding semantics in terms of labeled transition systems utilizing probabilistic matching graph. A variant of bisimulation (strictly stronger than hyperbisimulation of the original FC) is defined and shown to be a congruence. We further enrich the existing axiomatic system of FC to provide algebraic laws to decide the equivalence between processes in the presence of errors in the occurrence of fusion actions. The enriched axiomatization is proved to be both sound and complete for finite processes.