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 (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.

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• 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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