Computing the Width of Non-deterministic Automata

@article{Kuperberg2019ComputingTW,
  title={Computing the Width of Non-deterministic Automata},
  author={Denis Kuperberg and Anirban Majumdar},
  journal={ArXiv},
  year={2019},
  volume={abs/1811.00483}
}
We introduce a measure called width, quantifying the amount of nondeterminism in automata. Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly on any accepted input. We describe an incremental determinisation construction on NFAs, which can be more efficient than the full powerset determinisation, depending on the width of the input NFA. This construction can be generalised to infinite words, and… 
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References

SHOWING 1-10 OF 37 REFERENCES
Width of Non-deterministic Automata
TLDR
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.
How Deterministic are Good-For-Games Automata?
TLDR
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.
On the complexity of omega -automata
  • S. Safra
  • Computer Science
    [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
TLDR
The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case, and can be used to obtain an improved complementation construction for Buchi automata that is essentially optimal.
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…
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…
Generalized simulation relations with applications in automata theory
TLDR
The central topic of this thesis is the design of GFQ equivalences for Buchi automata, and how simulation relations have recently been applied to significantly optimize exact (exponential) language inclusion algorithms, thus extending their practical applicability.
The complexity of tree automata and logics of programs
  • E. Emerson, C. Jutla
  • Computer Science
    [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
TLDR
It is shown that for tree automata with m states and n pairs nonemptiness can be tested in time O((mn)/sup 3n/), even though the problem is in general NP-complete, and it follows that satisfiability for propositional dynamic logic with a repetition construct and for the propositional mu-calculus can be tests in deterministic single exponential time.
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.
Structurally Unambiguous Finite Automata
TLDR
It is shown that SUFA can be exponentially more succinct in the number of states than UFA and MDFA (deterministic finite automata with multiple initial states).
Are Good-for-Games Automata Good for Probabilistic Model Checking?
TLDR
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.
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