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arXiv · 2608.10583

Weak Bisimulation Finiteness of Pushdown Systems With Deterministic $\varepsilon$-Transitions Is 2-ExpTime-Complete

Stefan Göller·Paweł Parys
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Abstract

We consider the problem of deciding whether a given pushdown system all of whose $\varepsilon$-transitions are deterministic is weakly bisimulation finite, that is, whether it is weakly bisimulation equivalent to a finite system. We prove that this problem is 2-ExpTime-complete. This consists of three elements: First, we prove that the smallest finite system that is weakly bisimulation equivalent to a fixed pushdown system, if exists, has size at most doubly exponential in the description size of the pushdown system. Second, we propose a fast algorithm deciding whether a given pushdown system is weakly bisimulation equivalent to a finite system of a given size. Third, we prove 2-ExpTime-hardness of the problem. The problem was known to be decidable, but the previous algorithm had Ackermannian complexity (6-ExpSpace in the easier case of pushdown systems without $\varepsilon$-transitions); concerning lower bounds, only ExpTime-hardness was known.

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Stefan Göller, Paweł Parys. 2026-08-11. Weak Bisimulation Finiteness of Pushdown Systems With Deterministic $\varepsilon$-Transitions Is 2-ExpTime-Complete. https://doi.org/10.1137/1.9781611977554.ch105

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