Decidability of Split Equivalence

Abstract

We show that the following problem is decidable: given expressions E 1 and E 2 constructed from variables by the regular operations and shuffle, is the identity E 1 = E 2 true for all instantiations of its variables by strings? Our proof uses the notations developed in the causal approach to concurrency. As a byproduct we obtain decidability of similar equivalence for other formalisms. In particular, we prove decidability of split equivalence for Petri nets. Our paper also provides an alternative proof for a characterization of split equivalence recently given by W.Vogler.