Institut de Mathématiques de Marseille, UMR 7373


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A realizability notion for MSO over ω

Jeudi 7 décembre 11:00-12:30 - Pierre PRADIC - LIP, ENS Lyon

A realizability notion for MSO over ω

Résumé : 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.

Lieu : Salle des séminaires 304-306 (3ème étage) - Institut de Mathématiques de Marseille (UMR 7373)
Site Sud - Bâtiment TPR2
Campus de Luminy, Case 907
13288 MARSEILLE Cedex 9

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