Checking History-Determinism is NP-hard for Parity Automata
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.
Cite
@article{arxiv.2310.13498,
title = {Checking History-Determinism is NP-hard for Parity Automata},
author = {Keya Prakash},
journal= {arXiv preprint arXiv:2310.13498},
year = {2026}
}
Comments
Full version of the paper accepted at FoSSaCS 2024. Some minor editorial changes from the previous version following suggestions from anonymous reviewers