Characterizing polynomial and exponential complexity classes in elementary lambda-calculus.
Résumé
In this paper an implicit characterization of the complexity classes kEXP and kFEXP, for k >=0, is given, by a type assignment system for a stratified lambda-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 kEXP is characterized by a hierarchy of types.