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LSV Seminars
http://www.lsv.ens-cachan.fr
Seminars of the Laboratoire Spécification et Vérification at ENS Cachanhttp://www.lsv.ens-cachan.fr/Seminaires/2017-05-28T14:06:16+02:00daily6Colin Riba: A Curry-Howard Approach to Tree Automata
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201706131100
This talk surveys a Curry-Howard perspective on Rabin's
Tree Theorem, the decidability of Monadic Second-Order Logic (MSO) on infinite trees.
Rabin's Tree Theorem proceeds by effective translations of MSO-formulae to tree automata.
The operations on tree automata used in these translations can be organized in a deduction
system based on intuitionistic linear logic (ILL). We propose a computational interpretation
of this deduction system along the lines of the Curry-Howard proofs-as-programs correspondence.
Relying on the usual technology of game semantics, we interpret proofs as strategies
in two-player games generalizing usual acceptance games of tree automata.
This realizability semantics satisfies an expected property of witness extraction
from proofs of existential statements. It also allows to combine realizers produced
as interpretations of proofs with strategies witnessing (non-)emptiness of tree
automata, possibly obtained using external algorithms. Moreover, an adaptation
of a usual construction for the simulation of alternating automata by non-deterministic
ones satisfies the deduction rules of the "of course" exponential modality of ILL. Pablo Arrighi: TBA
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201706201100
Thomas Wies: TBA
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201706271100
Raul Fervari: TBA
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201707111100
Dietrich Kuske: TBA
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201710031100