A Dialectica-Like Interpretation of a Linear MSO on Infinite Words - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2019

A Dialectica-Like Interpretation of a Linear MSO on Infinite Words

Résumé

We devise a variant of Dialectica interpretation of intuition-istic linear logic for LMSO, a linear logic-based version MSO over infinite words. LMSO was known to be correct and complete w.r.t. Church's synthesis , thanks to an automata-based realizability model. Invoking Büchi-Landweber Theorem and building on a complete axiomatization of MSO on infinite words, our interpretation provides us with a syntactic approach , without any further construction of automata on infinite words. Via Dialectica, as linear negation directly corresponds to switching players in games, we furthermore obtain a complete logic: either a closed formula or its linear negation is provable. This completely axiomatizes the theory the realizability model of LMSO. Besides, this shows that in principle, one can solve Church's synthesis for a given ∀∃-formula by only looking for proofs of either that formula or its linear negation.
Fichier principal
Vignette du fichier
churchdial.pdf (591.16 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01925701 , version 1 (17-11-2018)

Identifiants

  • HAL Id : hal-01925701 , version 1

Citer

Cécilia Pradic, Colin Riba. A Dialectica-Like Interpretation of a Linear MSO on Infinite Words. FOSSACS'19, Apr 2019, Prague, Czech Republic. ⟨hal-01925701⟩
73 Consultations
133 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More