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The beyond worst-case synthesis problem was introduced recently by Bruyère et al. [BFRR14]: it aims at building system controllers that provide strict worst-case performance guarantees against an antagonistic environment while ensuring higher expected performance against a stochastic model of the environment. Our work extends the framework of [BFRR14] and follow-up papers, which focused on quantitative objectives, by addressing the case of ω-regular conditions encoded as parity objectives, aarXiv:1702.05472v2 fatcat:ptukr7d7crbw7apxqoq2fboueq