Computing Adequately Permissive Assumptions for Synthesis
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We solve the problem of automatically computing a new class of environment assumptions in two-player turn-based finite graph games which characterize an “adequate cooperation” needed from the environment to allow the system player to win. Given an ω-regular winning condition Φ for the system player, we compute an ω-regular assumption Ψ for the environment player, such that (i) every environment strategy compliant with Ψ allows the system to fulfill Φ (sufficiency), (ii) Ψ can be fulfilled by the environment for every strategy of the system (implementability), and (iii) Ψ does not prevent any cooperative strategy choice (permissiveness). For parity games, which are canonical representations of ω-regular games, we present a polynomial-time algorithm for the symbolic computation of adequately permissive assumptions and show that our algorithm runs faster and produces better assumptions than existing approaches – both theoretically and empirically. To the best of our knowledge, for ω-regular games, we provide the first algorithm to compute sufficient and implementable environment assumptions that are also permissive.
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