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arXiv · 2310.13498

Checking History-Determinism is NP-hard for Parity Automata

Keya Prakash
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Abstract

We show that the problem of checking if a given nondeterministic parity automaton simulates another given nondeterministic parity automaton is NP-hard. We then adapt the techniques used for this result to show that the problem of checking history-determinism for a given parity automaton is NP-hard. This is an improvement from Kuperberg and Skrzypczak's previous lower bound of solving parity games from 2015. We also show that deciding if Eve wins the one-token game or the two-token game of a given parity automaton is NP-hard. Finally, we show that the problem of deciding if the language of a nondeterministic parity automaton is contained in the language of a history-deterministic parity automaton can be solved in quasi-polynomial time.

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Keya Prakash. 2023-10-20. Checking History-Determinism is NP-hard for Parity Automata. https://arxiv.org/abs/2310.13498

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