On paths-based criteria for polynomial time complexity in proof-nets

Matthieu Perrinel (1, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages

Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way the class Ptime. In this paper we study the complexity of linear logic proof-nets and propose two sufficient criteria, one for elementary time soundness and the other one for Ptime soundness, based on the study of paths inside the proof-net. These criteria offer several benefits: they provide a bound for any reduction sequence and they can be used to prove the complexity soundness of several variants of linear logic. As an example we show with our criteria a strong polytime bound for the system L^4 (light linear logic by levels).

Mots clés: context semantics; polynomial time; linear logic; light logics; implicit computational complexity

Domaines: Logique en informatique [cs.LO]

Matthieu Perrinel. On paths-based criteria for polynomial time complexity in proof-nets. Foundational and Practical Aspects of Resource Analysis (FOPARA) 2013, Aug 2013, Bertinoro, Italy. pp.127--142, ⟨10.1007/978-3-319-12466-7_8⟩. ⟨hal-00992578⟩