Bisimulation Equivalence of First-Order Grammars is ACKERMANN-Complete

Petr Jančar; Sylvain Schmitz

doi:10.1109/LICS.2019.8785848

paper

Bisimulation Equivalence of First-Order Grammars is ACKERMANN-Complete

arXiv:1901.07170 · doi:10.1109/LICS.2019.8785848

Abstract

Checking whether two pushdown automata with restricted silent actions are weakly bisimilar was shown decidable by Sénizergues (1998, 2005). We provide the first known complexity upper bound for this famous problem, in the equivalent setting of first-order grammars. This ACKERMANN upper bound is optimal, and we also show that strong bisimilarity is primitive-recursive when the number of states of the automata is fixed.