Characterizing Polynomial and Exponential Complexity Classes in Elementary Lambda-Calculus

Abstract : In 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.
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Josep Diaz; Ivan Lanese; Davide Sangiorgi. 8th IFIP International Conference on Theoretical Computer Science (TCS), Sep 2014, Rome, Italy. Springer, Lecture Notes in Computer Science, LNCS-8705, pp.151-163, 2014, Theoretical Computer Science. <10.1007/978-3-662-44602-7_13>
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Patrick Baillot, Erika De Benedetti, Simona Ronchi Della Rocca. Characterizing Polynomial and Exponential Complexity Classes in Elementary Lambda-Calculus. Josep Diaz; Ivan Lanese; Davide Sangiorgi. 8th IFIP International Conference on Theoretical Computer Science (TCS), Sep 2014, Rome, Italy. Springer, Lecture Notes in Computer Science, LNCS-8705, pp.151-163, 2014, Theoretical Computer Science. <10.1007/978-3-662-44602-7_13>. <hal-01015171v2>

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