On the Expressiveness of the Choice Quanti erBas

We deene process algebras with a generalised operation P for choice. For every innnite cardinal , we prove that the algebra of transition trees with branching degree < is free in the class of process algebras in which P is deened for all subsets with a cardinality <. We explain how the expressions of a fragment of the speciication language CRL may be used to denote elements of our process algebras. In particular, we explain how choice quantiiers may be used to denote innnite sums. We show that choice quantiiers can simulate both the existential and the universal quantiiers of rst-order logic, while the input preex mechanism can only simulate the universal quantiier.