Alternative quanti cation vs . input pre xingJan

This is a summary of our paper \Process algebras with alternative quantii-cation over data" (Groote and Luttik (1998)). In this paper, we deene a class of process algebras with a generalised operation P that allows explicit treatment of alternative quantiication over data, and investigate the speciic subclass formed by the algebras of nite processes modulo strong bisimulation. We have shown that, in such algebras, equality between nite processes is deenable by means of a rst-order data formula, and that, if the data is computable and has a built-in equality predicate, any 0 4 data formula is deenable by means of an equation between ground process terms. Hence, equality in strong bisimulation algebras with a computable data part is 0 4-hard. We have also investigated a restricted version of alternative quantiication: the input preex mechanism of Parrow and Sangiorgi (1995) and Hennessy and Lin (1996). This restriction, for computable data with a built-in equality predicate , yields a less expressive formalism, namely equality in the strong bisimu-lation algebra coincides with the universal fragment of rst-order logic for the data; so the input preex mechanism gives rise to strong bisimulation algebras for which equality is complete in 0 1. 1 Process algebras with alternative quantiication A process algebra is an algebra that contains a universe P and binary operations + + + and on P such that hP;+ + +i is a semilattice, hP; i is a semigroup, and distributes from the right over + + +. The operation + + + is used to model alternative composition, a nondeterministic choice between its arguments, and stands for sequential composition, performing its second argument upon completion of its rst. A many-sorted process algebra that does not contain operations that take the sort of processes into some other sort, is often called a process algebra with data; the