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International Conference on Concurrency Theory

CONCUR 2014: CONCUR 2014 – Concurrency Theory pp 544–559Cite as

Qualitative Concurrent Parity Games: Bounded Rationality

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8704))

Abstract

We study two-player concurrent games on finite-state graphs played for an infinite number of rounds, where in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. The objectives are ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). While the qualitative analysis problem for concurrent parity games with infinite-memory, infinite-precision randomized strategies was studied before, we study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision, or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory, or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in \(\mathcal{O}(n^{2d+3})\) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. Our symbolic algorithms are based on a characterization of the winning sets as μ-calculus formulas, however, our μ-calculus formulas are crucially different from the ones for concurrent parity games (without bounded rationality); and our memoryless witness strategy constructions are significantly different from the infinite-memory witness strategy constructions for concurrent parity games.

The research was partly supported by FWF Grant No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.

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Authors and Affiliations

  1. IST, Austria

    Krishnendu Chatterjee

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  1. Krishnendu Chatterjee
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Editors and Affiliations

  1. Department of Mathematics, University of Padova, Via Trieste, 63, 35121, Padova, Italy

    Paolo Baldan

  2. Department of Computer Science, University of Roma “La Sapienza”, Via Salaria, 113, 00198, Rome, Italy

    Daniele Gorla

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Chatterjee, K. (2014). Qualitative Concurrent Parity Games: Bounded Rationality. In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_37

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  • DOI: https://doi.org/10.1007/978-3-662-44584-6_37

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