Strategy Construction in Infinite Ganes with Streett and Rabin Chain Winning Conditions

@inproceedings{Buhrke1996StrategyCI,
  title={Strategy Construction in Infinite Ganes with Streett and Rabin Chain Winning Conditions},
  author={Nils Buhrke and Helmut Lescow and Jens V{\"o}ge},
  booktitle={TACAS},
  year={1996}
}
We consider finite-state games as a model of nonterminating reactive computations. A natural type of specification is given by games with Streett winning condition (corresponding to automata accepting by conjunctions of fairness conditions). We present an algorithm which solves the problem of program synthesis for these specifications. We proceed in two steps: First, we give a reduction of Streett automata to automata with the Rabin chain (or parity) acceptance condition. Secondly, we develop… 

Implementation of a Strategy Improvement Algorithm for Finite-State Parity Games

TLDR
The emphasis of the paper is the development of a user interface which supports the researcher in case studies for algorithms of ω-automata theory and evaluating the (so far open) asymptotic runtime of the presented algorithm.

Memory and delay in regular infinite games

TLDR
The problem whether a given regular specification is solvable by a continuous operator is decidable and that each continuous solution can be reduced to one of bounded lookahead, and the concept of strategies is introduced, which derives a generalized determinacy of regular conditions.

Synthesis of winning strategies for interaction under partial information

TLDR
This work adresses the strategy problem for multiplayer games with imperfect information which are of infinite duration and have (up to) contextfree winning conditions and provides a complete characterization of all communication graphs for which synthesis is decidable for locally decomposable regular and contextfree specifications.

Faster Algorithms for Finitary Games

The theory of games is a prominent tool in the controller synthesis problem. The class of ω-regular games, in particular, offers a clear and robust model of specifications, and present an alternative

A Hybrid Algorithm for LTL Games

TLDR
This work presents a practical hybrid algorithm--a combination of symbolic and explicit algorithm--for the computation of winning strategies for unrestricted LTL games that has been successfully applied to synthesize reactive systems with up to 1011 states.

Dicing on the Streett

Alternating Good-for-MDP Automata

TLDR
The surprising answer is that the alternating good-for-MDP automata produced from deterministic Streett automata are bi-linear in the the size of the deterministic automaton and its index, and can therefore be exponentially more succinct than minimal nondeterministic B¨uchi automata.

Streett Automata Model Checking of Higher-Order Recursion Schemes

TLDR
Besides being able to directly deal with Streett automata, this algorithm is the first practical Streett or parity automata model checking algorithm that runs in time polynomial in the size of HORS, assuming that the other parameters are fixed.

Computation of winning strategies for μ-calculus by fixpoint iteration

TLDR
An implementation of a model checker for μ-Calculus that certifies its result as a winning strategy for a corresponding parity game by means of a fixpoint iteration, similar to the well-known set semantics of μ-calculus.

Certification for μ-calculus with winning strategies Category : Research Paper

TLDR
Memory-efficient certificates for μ-calculus model checking problems based on the well-known correspondence of μ-Calculus modelchecking with winning certain parity games are defined and a prototypical implementation of a μ- Calculus model checker generating these certificates has been developed.

References

SHOWING 1-10 OF 46 REFERENCES

Control of Infinite Behavior of Finite Automata

TLDR
The results represent a direct, efficient and natural solution to Church's problem, the construction of winning strategies for two-player zero-sum $\omega$-regular games of perfect information, and the emptiness problem for automata on infinite trees.

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

Trees, automata, and games

TLDR
This work gives here an alternative and transparent proof of Rabin's result on tree automata, which is based on ideas of his predecessors and especially those of B- and-uuml;chi-&-mdash;.

On the Synthesis of Strategies in Infinite Games

TLDR
The automata theoretic setting of infinite games (given by “game graphs”), a new construction of winning strategies in finite-state games, and some questions which arise for games over effectively presented infinite graphs are described.

Automata on Infinite Objects

  • W. Thomas
  • Computer Science
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990

Tree automata, mu-calculus and determinacy

  • E. EmersonC. Jutla
  • Mathematics, Computer Science
    [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
  • 1991
TLDR
It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees, which provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results.

Exponential determinization for ω-automata with strong-fairness acceptance condition (extended abstract)

TLDR
The results imply that Streett automata can be used instead of Bu¨chi automata (with the weaker acceptance condition) without any loss of efficiency, and show an exponential determinization construction for any Streett Automaton.

Propositional Dynamic Logic of looping and converse

Propositional Dynamic Logic can be extended to include both an infinitary iteration construct delta and a backtracking construct converse. The resulting logic does not satisfy the finite model