Büchi Good-for-Games Automata Are Efficiently Recognizable

  title={B{\"u}chi Good-for-Games Automata Are Efficiently Recognizable},
  author={Marc Bagnol and Denis Kuperberg},
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 information about the remaining suffix of the word. These automata can be used to solve games with ω-regular conditions, and in particular were introduced as a tool to solve Church's synthesis problem. We focus here on the problem of recognizing Buchi GFG automata, that we call Buchi GFGness problem: given… 

Figures from this paper

On Succinctness and Recognisability of Alternating Good-for-Games Automata
The complexity of deciding "half-GFGness", a property specific to alternating automata that only requires nondeterministic choices to be resolved in an online manner, is studied, and it is shown that this problem is strictly more difficult than GFGness check.
Minimising Good-for-Games automata is NP complete
It is shown for the standard state based acceptance that the minimality of a GFG automaton is NP-complete for Buchi, Co-Buchi, and parity G FG automata, a surprisingly straight forward generalisation of the proofs from deterministic Buchi automata.
Minimization and Canonization of GFG Transition-Based Automata
The minimization algorithm is described and used to show canonicity for transition-based GFG co-B¨uchi word automata: all minimal automata have isomorphic safe components and once the authors saturate the automata with α -transitions, they get full isomorphism.
On the Succinctness of Alternating Parity Good-for-Games Automata
This work presents a single exponential determinisation procedure and an Exptime upper bound to the problem of recognising whether an alternating automaton is GFG, and studies the complexity of deciding "half-GFGness", a property specific to alternating automata that only requires nondeterministic choices to be resolved in an online manner.
Canonicity in GFG and Transition-Based Automata
Limiting attention to the safe components is useful, and implies that the only minimal tDCWs that have no canonical form are these for which the transition to the GFG model results in strictly smaller automaton, which do have a canonical minimal form.
On (I/O)-Aware Good-For-Games Automata
(I/O)-aware GFG automata are unboundedly more succinct than deterministic and even GFG automation, using them circumvents determinization, and their study leads to new and interesting insights about hostile vs. collaborative nondeterminism, as well as the theoretical bound for realizing systems.
Token Games and History-Deterministic Quantitative-Automata
A nondeterministic automaton is history-deterministic if its nondeterminism can be resolved by only considering the prefix of the word read so far. Due to their good compositional properties,
Computing the Width of Non-deterministic Automata
It is shown that computing the width of an automaton is EXPTime-complete, which implies EXPTIME-completeness for multipebble simulation games on NFAs, and shows that checking whether a coB\"uchi automata is determinisable by pruning is NP-complete.
Good-for-games ω-Pushdown Automata
These are automata whose nondeterminism can be resolved based on the run constructed thus far and it follows that the universality problem for ω-GFG-PDA is in EXPTIME as well.
A Hierarchy of Nondeterminism
It is shown that the hierarchy is strict, the expressive power of the different levels in it is studied, as well as the complexity of deciding the membership of a language in a given level, which relates the level of nondeterminism with the probability that a random run on a word in the language is accepting.


How Deterministic are Good-For-Games Automata?
GFG automata enjoy the benefits of typeness, similarly to the case of deterministic automata, and are shown to be exponentially more succinct than deterministic ones.
Solving Games Without Determinization
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.
Width of Non-deterministic Automata
It is shown by proving that checking whether a coBuchi automaton is determinisable by pruning is NP-complete, and on finite or infinite words, it is shown that computing the width of an automaton are PSPACE-hard.
Are Good-for-Games Automata Good for Probabilistic Model Checking?
It is shown how good-for-games automata can be used for the quantitative analysis of systems modeled by Markov decision processes against ω-regular specifications and evaluated by a series of experiments.
A Hierarchy of Polynomial-Time Computable Simulations for Automata
We define and provide algorithms for computing a natural hierarchy of simulation relations on the state-spaces of ordinary transition systems, finite automata, and Buchi automata.T hese simulations
On Determinisation of Good-for-Games Automata
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.
Nondeterminism in the Presence of a Diverse or Unknown Future
It is shown that GFT=GFG⊃DBP, and described a determinization construction for GFG automata, which shows the possible succinctness of GFG and GFT automata compared to deterministic automata.
Small Progress Measures for Solving Parity Games
A new algorithm for deciding the winner in parity games, and hence also for the modal µ-calculus model checking, based on a notion of game progress measures, characterized as pre-fixed points of certain monotone operators on a complete lattice.
Solving sequential conditions by finite-state strategies
Our main purpose is to present an algorithm which decides whether or not a condition 𝕮(X, Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This
Deciding parity games in quasipolynomial time
It is shown that the parity game can be solved in quasipolynomial time and it is proven that coloured Muller games with n nodes and m colours can be decided in time O((mm · n)5); it is also shown that this bound cannot be improved to O((2m · n), for any c, unless FPT = W[1].