Citation
Krishnendu Chatterjee, Luca de Alfaro, Tom Henzinger. "The Complexity of Quantitative Concurrent Parity Games". SODA, 2006.

Abstract
We consider two-player infinite games played on graphs. The games are concurrent, in that at each state the players choose their moves simultaneously and independently, and stochastic, in that the moves determine a probability distribution for the successor state. The value of a game is the maximal probability with which a player can guarantee the satisfaction of her objective. We show that the values of concurrent games with \omega-regular objectives expressed as parity conditions can be decided in NP and coNP. This result substantially improves the best known previous bound of 3EXPTIME. It also shows that the full class of concurrent parity games is no harder than the special case of turn-based stochastic reachability games, for which NP and coNP is the best known bound. While the previous, more restricted NP and coNP results for graph games relied on the existence of particularly simple (pure memoryless) optimal strategies, in concurrent games with parity objectives optimal strategies may not exist, and e-optimal strategies (which achieve the value of the game within a parameter e > 0) require in general both randomization and infinite memory. Hence our proof must rely on a more detailed analysis of strategies and, in addition to the main result, yields two results that are interesting on their own. First, we show that there exist e-optimal strategies that in the limit coincide with memoryless strategies; this parallels the celebrated result of Mertens-Neyman for concurrent games with limit-average objectives. Second, we complete the characterization of the memory requirements for e-optimal strategies for concurrent games with parity conditions, by showing that memoryless strategies suffice for e-optimality for coBüchi conditions.

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  Krishnendu Chatterjee, Luca de Alfaro, Tom Henzinger. <a
  href="http://chess.eecs.berkeley.edu/pubs/79.html"
  >The Complexity of Quantitative Concurrent Parity
  Games</a>, SODA, 2006.

• Plain text

  Krishnendu Chatterjee, Luca de Alfaro, Tom Henzinger.
  "The Complexity of Quantitative Concurrent Parity
  Games". SODA, 2006.

• BibTeX

  @inproceedings{ChatterjeeAlfaroHenzinger06_ComplexityOfQuantitativeConcurrentParityGames,
      author = {Krishnendu Chatterjee and Luca de Alfaro and Tom
                Henzinger},
      title = {The Complexity of Quantitative Concurrent Parity
                Games},
      booktitle = {SODA},
      year = {2006},
      abstract = {We consider two-player infinite games played on
                graphs. The games are concurrent, in that at each
                state the players choose their moves
                simultaneously and independently, and stochastic,
                in that the moves determine a probability
                distribution for the successor state. The value of
                a game is the maximal probability with which a
                player can guarantee the satisfaction of her
                objective. We show that the values of concurrent
                games with \omega-regular objectives expressed as
                parity conditions can be decided in NP and coNP.
                This result substantially improves the best known
                previous bound of 3EXPTIME. It also shows that the
                full class of concurrent parity games is no harder
                than the special case of turn-based stochastic
                reachability games, for which NP and coNP is the
                best known bound. While the previous, more
                restricted NP and coNP results for graph games
                relied on the existence of particularly simple
                (pure memoryless) optimal strategies, in
                concurrent games with parity objectives optimal
                strategies may not exist, and e-optimal strategies
                (which achieve the value of the game within a
                parameter e > 0) require in general both
                randomization and infinite memory. Hence our proof
                must rely on a more detailed analysis of
                strategies and, in addition to the main result,
                yields two results that are interesting on their
                own. First, we show that there exist e-optimal
                strategies that in the limit coincide with
                memoryless strategies; this parallels the
                celebrated result of Mertens-Neyman for concurrent
                games with limit-average objectives. Second, we
                complete the characterization of the memory
                requirements for e-optimal strategies for
                concurrent games with parity conditions, by
                showing that memoryless strategies suffice for
                e-optimality for coBüchi conditions. },
      URL = {http://chess.eecs.berkeley.edu/pubs/79.html}
  }
  

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