Combining Linear Logic and Size Types for Implicit Complexity

Abstract

International audienceSeveral type systems have been proposed to statically control the time complexity of lambdacalculusprograms and characterize complexity classes such as FPTIME or FEXPTIME. A firstline of research stems from linear logic and restricted versions of its !-modality controlling duplication.A second approach relies on the idea of tracking the size increase between input and output,and together with a restricted recursion scheme, to deduce time complexity bounds. Howeverboth approaches suffer from limitations : either a limited intensional expressivity, or linearityrestrictions. In the present work we incorporate both approaches into a common type system, inorder to overcome their respective constraints. Our system is based on elementary linear logiccombined with linear size types, called sEAL, and leads to characterizations of the complexityclasses FPTIME and 2k-FEXPTIME, for k >= 0