This paper presents a new format for process algebras, the extended tyft/tyxt format which generalises the tyft/tyxt format of Groote and Vaandrager. The format differs from most previous formats in that the labels on transitions are treated as many-sorted terms. Bisimulation is a congruence for all operators defined in this format.
When one extended transition system specification is summed with another, the resulting bisimulation can either identify more terms (an abstracting extension up to bisimulation) or fewer terms (a refining extension up to bisimulation) than the original bisimulation on the individual system. The notions of abstracting extension and refining extension are defined, and two theorems are presented giving conditions required for achieving each type of extension. These results provide a way to compare different semantic equivalences defined for different process algebras.
Finally, an application of this theory to semantic equivalence comparison is given for a new result relating Castellani's pomset equivalence and Krishnan's multiprocessor equivalence.
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