Characterizing Polynomial and Exponential Complexity Classes in Elementary Lambda-Calculus

Part 2: Track B: Logic, Semantics, Specification and VerificationInternational audienceIn this paper an implicit characterization of the complexity classes k-EXP and k-FEXP, for k ≥ 0, is given, by a type assignment system for a stratified λ-calculus, where types for programs are witnesses of the corresponding complexity class. Types are formulae of Elementary Linear Logic (ELL), and the hierarchy of complexity classes k-EXP is characterized by a hierarchy of types