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Finitary Winning in \omega-Regular Games
Krishnendu Chatterjee, Tom Henzinger

Citation
Krishnendu Chatterjee, Tom Henzinger. "Finitary Winning in \omega-Regular Games". TACAS, March, 2006.

Abstract
Games on graphs with \omega-regular objectives provide a model for the control and synthesis of reactive systems. Every \omega-regular objective can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens eventually. Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (B├╝chi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett (fairness) objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound.

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Citation formats  
  • HTML
    Krishnendu Chatterjee, Tom Henzinger. <a
    href="http://chess.eecs.berkeley.edu/pubs/82.html"
    >Finitary Winning in \omega-Regular Games</a>,
    TACAS, March, 2006.
  • Plain text
    Krishnendu Chatterjee, Tom Henzinger. "Finitary Winning
    in \omega-Regular Games". TACAS, March, 2006.
  • BibTeX
    @inproceedings{ChatterjeeHenzinger06_FinitaryWinningInomegaRegularGames,
        author = {Krishnendu Chatterjee and Tom Henzinger},
        title = {Finitary Winning in \omega-Regular Games},
        booktitle = {TACAS},
        month = {March},
        year = {2006},
        abstract = {Games on graphs with \omega-regular objectives
                  provide a model for the control and synthesis of
                  reactive systems. Every \omega-regular objective
                  can be decomposed into a safety part and a
                  liveness part. The liveness part ensures that
                  something good happens eventually. Two main
                  strengths of the classical, infinite-limit
                  formulation of liveness are robustness
                  (independence from the granularity of transitions)
                  and simplicity (abstraction of complicated time
                  bounds). However, the classical liveness
                  formulation suffers from the drawback that the
                  time until something good happens may be
                  unbounded. A stronger formulation of liveness,
                  so-called finitary liveness, overcomes this
                  drawback, while still retaining robustness and
                  simplicity. Finitary liveness requires that there
                  exists an unknown, fixed bound b such that
                  something good happens within b transitions. While
                  for one-shot liveness (reachability) objectives,
                  classical and finitary liveness coincide, for
                  repeated liveness (Büchi) objectives, the
                  finitary formulation is strictly stronger. In this
                  work we study games with finitary parity and
                  Streett (fairness) objectives. We prove the
                  determinacy of these games, present algorithms for
                  solving these games, and characterize the memory
                  requirements of winning strategies. Our algorithms
                  can be used, for example, for synthesizing
                  controllers that do not let the response time of a
                  system increase without bound.},
        URL = {http://chess.eecs.berkeley.edu/pubs/82.html}
    }
    

Posted by Krishnendu Chatterjee, PhD on 9 May 2006.
Groups: chess
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