Actions speak louder than words: Proving bisimilarity for context-free processes

Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant context-free grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goal-directed rules. The decision procedure also provides the essential part of the bisimulation relation between two processes which underlies their equivalence. We also show how to obtain a sound and complete sequent-based equational theory for such processes from the tableau system and how one can extract what Caucal calls a fundamental relation from a successful tableau.