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Elementary linear logic revisited for polynomial time and an exponential time hierarchy (extended version)

Patrick Baillot 1

(19/09/2011)

Elementary linear logic is a simple variant of linear logic, introduced by Girard and which characterizes in the proofs-as-programs approach the class of elementary functions (computable in time bounded by a tower of exponentials of fixed height). Our goal here is to show that despite its simplicity, elementary linear logic can nevertheless be used as a common framework to characterize the different levels of a hierarchy of deterministic time complexity classes, within elementary time. We consider a variant of this logic with type fixpoints and weakening. By selecting specific types we then characterize the class P of polynomial time predicates and more generally the hierarchy of classes k-EXP, for k>=0, where k-EXP is the union of DTIME(2_k^{n^i}), for i>=1.

1 :	Laboratoire de l'Informatique du Parallélisme (LIP)
	Université de Lyon – CNRS : UMR5668 – INRIA – École Normale Supérieure - Lyon – Université Claude Bernard - Lyon I

Équipe de recherche : Plume

Domaine

:

Informatique/Logique en informatique

Mots Clés : linear logic – implicit computational complexity – proof-nets – polynomial time – lambda-calculus – type systems

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Contributeur : Patrick Baillot <>

Soumis le : Lundi 19 Septembre 2011, 16:10:44

Dernière modification le : Lundi 19 Septembre 2011, 16:14:41