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The parametric complexity of bisimulation equivalence of normed pushdown automata

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Abstract

Deciding bisimulation equivalence of two normed pushdown automata is one of the most fundamental problems in formal verification. The problem is proven to be ACKER-MANN-complete recently. Both the upper bound and the lower bound results indicate that the number of control states is an important parameter. In this paper, we study the parametric complexity of this problem. We refine previous results in two aspects. First, we prove that the bisimulation equivalence of normed PDA with two states is EXPTIME-hard. Second, we prove that the bisimulation equivalence of normed PDA with d states is in Fd+3, which improves the best known upper bound Fd+4 of this problem.

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Acknowledgements

This work was supported by the National Natural Foundation of China (Grant Nos. 62072299, 61872142, 61772336, 61572318) and the Open Project of Shanghai Key Laboratory of Trustworthy Computing (OP202102). We are grateful to the comments and suggestions of members of the BASICS lab. Special thanks to Professor Yuxi Fu for insightful discussions on this topic and support.

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Authors and Affiliations

  1. College of Information Technology, Shanghai Ocean University, Shanghai, 201306, China

    Wenbo Zhang

  2. BASICS Lab, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Wenbo Zhang

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  1. Wenbo Zhang
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Correspondence to Wenbo Zhang.

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Wenbo Zhang is a lecturer in College of Information Technology at Shanghai Ocean University, China. He received his PhD degree from Shanghai Jiao Tong University, China in 2020, supervised by Professor Yuxi Fu, and his BS degree from Southeast University, China in 2014. Currently his research interests include formal verification on infinite state systems, process algebra and automata theory.

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Zhang, W. The parametric complexity of bisimulation equivalence of normed pushdown automata. Front. Comput. Sci. 16, 164405 (2022). https://doi.org/10.1007/s11704-021-0340-x

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