A realizability notion for MSO over ω

Pierre Pradic

Date(s) : 07/12/2017   iCal
11 h 00 min - 12 h 30 min

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, at the price of a non-elementary complexity. 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 a realizability model inspired by Colin’s fibration of automatas over infinite trees. Extracting stream transducers from SMSO proofs is still non-elementary from an algorithmic point of view due to the rule of bounded comprehension.
Joint work with Colin Riba.



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