Bisimulation Equivalence of Pushdown Automata Is Ackermann-Complete

Authors Wenbo Zhang , Qiang Yin , Huan Long , Xian Xu

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Author Details

Wenbo Zhang
  • BASICS, Shanghai Jiao Tong University, Shanghai, China
Qiang Yin
  • Alibaba Group, Shanghai, China
Huan Long
  • BASICS, Shanghai Jiao Tong University, Shanghai, China
Xian Xu
  • East China University of Science and Technology, Shanghai, China


This work is supported by NSF of China (61772336, 61872142, 61572318). The authors are grateful to Yuxi Fu for insightful discussions on this topic and support. We also thank the anonymous reviewers for their helpful comments and suggestions.

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Wenbo Zhang, Qiang Yin, Huan Long, and Xian Xu. Bisimulation Equivalence of Pushdown Automata Is Ackermann-Complete. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 141:1-141:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Deciding bisimulation equivalence of two pushdown automata is one of the most fundamental problems in formal verification. Though Sénizergues established decidability of this problem in 1998, it has taken a long time to understand its complexity: the problem was proven to be non-elementary in 2013, and only recently, Jančar and Schmitz showed that it has an Ackermann upper bound. We improve the lower bound to Ackermann-hard, and thus close the complexity gap.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Formal languages and automata theory
  • PDA
  • Bisimulation
  • Equivalence checking


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