Non-deterministic Boolean Proof Nets

Virgile Mogbil (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

We introduce Non-deterministic Boolean proof nets to study the correspondence with Boolean circuits, a parallel model of computation. We extend the cut elimination of Non-deterministic Multiplicative Linear logic to a parallel procedure in proof nets. With the restriction of proof nets to Boolean types, we prove that the cut-elimination procedure corresponds to Non-deterministic Boolean circuit evaluation and reciprocally. We obtain implicit characterization of the complexity classes NP and NC (the efficiently parallelizable functions).

Mots clés: Implicit Computational Complexity; Linear Logic; Non-deterministic Boolean Circuits; Non-deterministic Boolean Proof Nets; Parallel Cut-elimination

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]

Virgile Mogbil. Non-deterministic Boolean Proof Nets. First International Workshop Foundational and Practical Aspects of Resource Analysis (FOPARA 2009), Nov 2009, Eindhoven, Netherlands. pp. 131-145, ⟨10.1007/978-3-642-15331-0⟩. ⟨hal-00122981v3⟩