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The Church Synthesis Problem with Metric Jenkins, Mark Ouaknine, Joël Rabinovich, Alexander Worrell, James Church's Problem monadic logic games uniformization Church's Problem asks for the construction of a procedure which, given a logical specification S(I,O) between input strings I and output strings O, determines whether there exists an operator F that implements the specification in the sense that S(I,F(I)) holds for all inputs I. Buechi and Landweber gave a procedure to solve Church's problem for MSO specifications and operators computable by finite-state automata. We consider extensions of Church's problem in two orthogonal directions: (i) we address the problem in a more general logical setting, where not only the specifications but also the solutions are presented in a logical system; (ii) we consider not only the canonical discrete time domain of the natural numbers, but also the continuous domain of reals. We show that for every fixed bounded length interval of the reals, Church's problem is decidable when specifications and implementations are described in the monadic second-order logics over the reals with order and the +1 function. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mark Jenkins and Joël Ouaknine and Alexander Rabinovich and James Worrell 2011 Is Part Of LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2011.307 urn:nbn:de:0030-drops-32390 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.307 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode