Non deterministic Linear logic: application to Boolean circuits

Virgile Mogbil (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

Subsystems of Linear logic (LL) are used to give Curry- Howard characterizations of complexity classes as P. By expressing the non-determinism by an explicit rule to sum up, one characterizes NP [Mau03]. Following the Curry-Howard isomorphism but for parallel model of computation we study the proof nets of the non-deterministic multiplicative LL. Considering NNC(poly) i.e. NC (the efficiently parallelizable functions) with a polynomial amount of non-deterministic inputs, we define nmBN(poly) the uniform families of multiplicative Boolean proof nets with polynomial amount of explicit non-determinism. Finally nmBN(poly) is a Curry-Howard characterization of the complexity class NP = NNC(poly).

Mots clés: non-deterministic linear logic; implicit complexity; parallel cut-elimination; Boolean proof net; Boolean circuits

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

Virgile Mogbil. Non deterministic Linear logic: application to Boolean circuits. 2007. ⟨hal-00122981v1⟩