Bisimulation Equivalence Is Decidable for All Context-Free Processes

Abstract

A result originally due to Baeten, Bergstra, and Klop shows that strong bisimulation equivalence for normed BPA processes is decidable. On the other hand, Huynh and Tian, and Groote and Hüttel, have proved that all other standard equivalences are undecidable for normed BPA and thus for BPA in general, The open problem remaining has been whether bisimulation is decidable for the full BPA language. In this paper, we answer this question in the affirmative, using a proof technique based on the proof by Caucal of the decidability of language equivalence for simple algebraic grammars. The decision procedure relies on our main result, extending that of Caucal, that the maximal bisimulation of any BPA transition graph is finitely representable as a Thue congruence. The decision procedure consists of two semi-decision procedures, one testing for non-bisimilarity and one testing for bisimilarity.