Minimising good-for-games automata is NP-complete



Schewe, S ORCID: 0000-0002-9093-9518
(2020) Minimising good-for-games automata is NP-complete. .

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Abstract

This paper discusses the hardness of finding minimal good-for-games (GFG) Büchi, Co-Büchi, and parity automata with state based acceptance. The problem appears to sit between finding small deterministic and finding small nondeterministic automata, where minimality is NP-complete and PSPACE-complete, respectively. However, recent work of Radi and Kupferman has shown that minimising Co-Büchi automata with transition based acceptance is tractable, which suggests that the complexity of minimising GFG automata might be cheaper than minimising deterministic automata. We show for the standard state based acceptance that the minimality of a GFG automaton is NP-complete for Büchi, Co-Büchi, and parity GFG automata. The proofs are a surprisingly straight forward generalisation of the proofs from deterministic Büchi automata: they use a similar reductions, and the same hard class of languages.

Item Type: Conference or Workshop Item (Unspecified)
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 22 Mar 2021 09:40
Last Modified: 18 Jan 2023 22:55
DOI: 10.4230/LIPIcs.FSTTCS.2020.56
Open Access URL: https://drops.dagstuhl.de/opus/volltexte/2020/1329...
URI: https://livrepository.liverpool.ac.uk/id/eprint/3117937