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oai:drops-oai.dagstuhl.de:7719 2025-05-14T15:23:01Z ddc:004 open_access

A Curry-Howard Approach to Church's Synthesis Pradic, Cécilia Riba, Colin Intuitionistic Arithmetic Realizability Monadic Second-Order Logic on Infinite Words Church's synthesis problem asks whether there exists a finite-state stream transducer satisfying a given input-output specification. For specifications written in Monadic Second-Order Logic over infinite words, Church's synthesis can theoretically be solved algorithmically using automata and games. We revisit Church's synthesis via the Curry-Howard correspondence by introducing SMSO, a non-classical subsystem of MSO, which is shown to be sound and complete w.r.t. synthesis thanks to an automata-based realizability model. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Cécilia Pradic and Colin Riba 2017 Is Part Of LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2017.30 urn:nbn:de:0030-drops-77198 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.30 eng https://creativecommons.org/licenses/by/3.0/legalcode