A Dialectica-Like Approach to Tree Automata - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2016

A Dialectica-Like Approach to Tree Automata

Résumé

We propose a fibred monoidal closed category of alternating tree automata. Our notion is based on Dialectica-like categories, suggested by the specific logical form of the transitions of alternating automata. The basic monoidal closed structure gives a realizability interpretation of proofs of a first-order multiplicative linear logic as winning strategies in corresponding acceptance games. Moreover, we show that the usual powerset operation translating an alternating automaton to an equivalent non-deterministic one satisfies the deduction rules of the '!' modality of linear logic. We thus get a deduction system for intuitionistic linear logic, which in particular gives deduction for minimal intuitionistic predicate logic via the Girard translation. Using a suitable negative translation based on the '?' modality, we can interpret proofs of minimal classical logic, and also get a weak form of completeness of our realizers wrt language inclusion.
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Dates et versions

hal-01261183 , version 1 (24-01-2016)
hal-01261183 , version 2 (07-07-2016)
hal-01261183 , version 3 (14-07-2016)
hal-01261183 , version 4 (08-11-2016)
hal-01261183 , version 5 (27-04-2017)
hal-01261183 , version 6 (29-01-2018)
hal-01261183 , version 7 (28-08-2018)
hal-01261183 , version 8 (12-03-2019)
hal-01261183 , version 9 (20-09-2019)
hal-01261183 , version 10 (15-10-2019)

Identifiants

  • HAL Id : hal-01261183 , version 1

Citer

Colin Riba. A Dialectica-Like Approach to Tree Automata. 2016. ⟨hal-01261183v1⟩
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