Undecidable Equivalences for Basic Process Algebra

A recent theorem 3, 7, 19] shows that strong bisimilarity is decidable for the class of normed BPA processes, which correspond to a class of context-free grammars generating the-free context-free languages. In 21] Huynh and Tian have shown that readiness and failure equivalence are undecidable for BPA processes. In this paper we examine all other equivalences in the linear/branching time hierarchy 13] and show that none of them are decidable for normed BPA processes.