# How Deterministic are Good-For-Games Automata?

@article{Boker2017HowDA, title={How Deterministic are Good-For-Games Automata?}, author={Udi Boker and Orna Kupferman and Michal Skrzypczak}, journal={ArXiv}, year={2017}, volume={abs/1710.04115} }

In GFG automata, it is possible to resolve nondeterminism in a way that only depends on the past and still accepts all the words in the language. The motivation for GFG automata comes from their adequacy for games and synthesis, wherein general nondeterminism is inappropriate. We continue the ongoing effort of studying the power of nondeterminism in GFG automata. Initial indications have hinted that every GFG automaton embodies a deterministic one. Today we know that this is not the case, and…

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## 15 Citations

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## References

SHOWING 1-10 OF 27 REFERENCES

Typeness for omega-regular Automata

- Computer ScienceInt. J. Found. Comput. Sci.
- 2006

A complete picture of typeness for the weak, Buchi, co-Buchi, Rabin, and Streett acceptance conditions is given, and its usefulness is discussed.

Nondeterminism in the Presence of a Diverse or Unknown Future

- Computer ScienceICALP
- 2013

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.

Deterministic w Automata vis-a-vis Deterministic Buchi Automata

- Computer ScienceISAAC
- 1994

It is proved that a deterministic L- (DLA) or Rabin automaton (DRA), unlike deterministic Muller or Streett automata, is Buchi-type if and only if its language is realizable as a DBA, which means DBA are as compact as DRA or DLA.

Solving Games Without Determinization

- Computer ScienceCSL
- 2006

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.

On Determinisation of Good-for-Games Automata

- Computer ScienceICALP
- 2015

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.

Safraless decision procedures

- Computer Science46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
- 2005

This paper translations are significantly simpler than the standard approach, less difficult to implement, and have practical advantages like being amenable to optimizations and a symbolic implementation, and it is shown that the approach yields better complexity bounds.

Rabin vs. Streett Automata

- Computer ScienceFSTTCS
- 2017

The open problem of translating deterministic Rabin and Streett automata to the weaker types of deterministic co-B\"uchi and B\"uchi automata is resolved, showing that the state blowup involved in these translations, when possible, is in $2^{\Theta(n)}$, whereas the size blowup is in $\TheTA(n^2)$.

Decision problems forω-automata

- Computer Science, MathematicsMathematical systems theory
- 2005

This paper considers various definitions for machines of this type, including ones introduced by Biichi and McNaughton, and classify the complexity of definable sets of sequences for each type of finite automaton.

From linear time to branching time

- Mathematics, Computer ScienceTOCL
- 2005

This article shows that a linear-time property can be specified in the alternation-free μ-calculus iff it can be recognized by a deterministic Büchi automaton, and studies the problem of deciding whether a Linear-time Property, specified by either an automaton or an LTL formula, can be translated to anAlternation- free μ-Calculus formula, and describes the translation.

Regular Cost Functions over Finite Trees

- Computer Science, Mathematics2010 25th Annual IEEE Symposium on Logic in Computer Science
- 2010

The theory of regular cost functions over finite trees is developed, aquantitative extension to the notion of regular languages of trees, and nondeterministic and alternating finite tree cost automata for describing cost functions are introduced.