Decidability of Weak Bisimilarity for a Subset of BPA

In this paper we use the tableau as a means to prove decidability of weak bisimulation for normed BPA. Decidability was proved for a restricted subclass, the totally normed processes by Hirshfeld [Hirshfeld, Y., Bisimulation trees and the decidability of weak bisimulations. In: INFINITY 1996. proceedings of the 1st International Workshop on Verification of Infinite State Systems, Germany, vol. 5]. However in the case that weak bisimilarity to be decidable is inequivalence is finitely approximable. In this paper we relax restriction of totally normedness and prove decidability of weak bisimilarity for a subset of normed BPA which permit the norm of BPA processes is zero.