Pradic, Pierre and Riba, Colin - A Curry-Howard Approach to Church's Synthesis

lmcs:4414 - Logical Methods in Computer Science, December 9, 2019, Volume 15, Issue 4 -
A Curry-Howard Approach to Church's Synthesis

Authors: Pradic, Pierre and Riba, Colin

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 (MSO) 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, an intuitionistic variant of MSO over infinite words, which is shown to be sound and complete w.r.t. synthesis thanks to an automata-based realizability model.

Volume: Volume 15, Issue 4
Published on: December 9, 2019
Submitted on: March 29, 2018
Keywords: Computer Science - Logic in Computer Science


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