Minimising Good-for-Games automata is NP complete

@inproceedings{Schewe2020MinimisingGA,
  title={Minimising Good-for-Games automata is NP complete},
  author={Sven Schewe},
  booktitle={FSTTCS},
  year={2020}
}
  • S. Schewe
  • Published in FSTTCS 26 March 2020
  • Computer Science
This paper discusses the hardness of finding minimal good-for-games (GFG) Buchi, Co-Buchi, 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-Buchi automata with transition based acceptance is tractable, which suggests that the complexity of minimising… 

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References

SHOWING 1-10 OF 12 REFERENCES
Beyond Hyper-Minimisation---Minimising DBAs and DPAs is NP-Complete
TLDR
The NP-completeness of the problem of minimising deterministic automata over finite and infinite words is established, and the introduction of almost equivalence is introduced, an equivalence class for strictly between language equivalence for deterministic \buchi\ or \cobuchi\ automata and language equivalenced automata.
Solving Games Without Determinization
TLDR
The main insight is that a nondeterministic automaton is good for solving games if it fairly simulates the equivalent deterministicAutomata are constructed that omit the determinization step in game solving and reactive synthesis.
Minimal NFA Problems are Hard
TLDR
The following basic minimization problem is studied: Given a DFA (deterministic FA), find a minimum equivalent FA (FA) that is Turing-complete and Turing-supervised.
Good for Games Automata: From Nondeterminism to Alternation
TLDR
It is shown that alternating G FG automata are as expressive as deterministic automata with the same acceptance conditions and indices, and that determinizing Buchi and co-Buchi alternating GFG automata involves a $2^{\Theta(n)}$ state blow-up.
Büchi Good-for-Games Automata Are Efficiently Recognizable
Good-for-Games (GFG) automata offer a compromise between deterministic and nondetermin-istic automata. They can resolve nondeterministic choices in a step-by-step fashion, without needing any
On Determinisation of Good-for-Games Automata
TLDR
The main results of this work answer the question whether parity GFG automata actually present an improvement in terms of state-complexity the number of states compared to the deterministic ones.
Solving games without determinization. In ZoltánÉsik, editor, Computer Science Logic
  • 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL
  • 2006
Minimising good-for-games automata is NP complete
  • CoRR, abs/2003.11979,
  • 2003
Minimising good-for-games automata is NP complete. CoRR, abs
  • 2003
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