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Rapport Année : 2011

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

Patrick Baillot

Résumé

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.
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Dates et versions

hal-00624742 , version 1 (19-09-2011)

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  • HAL Id : hal-00624742 , version 1

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Patrick Baillot. Elementary linear logic revisited for polynomial time and an exponential time hierarchy (extended version). 2011. ⟨hal-00624742⟩
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