Verification of Ptime reducibility for system F terms via Dual Light Affine Logic

TL;DR

This paper presents a polynomial-time procedure to type second-order lambda-terms in Dual Light Affine Logic, ensuring all typable terms are evaluable in polynomial time and represent Ptime functions.

Contribution

It introduces a polynomial-time method for decorating System F terms into DLAL, enabling verification of polynomial-time reducibility.

Findings

Procedure runs in polynomial time relative to the original term size.

All DLAL-typed terms correspond to polynomial-time computable functions.

The method effectively bridges System F and DLAL typing systems.

Abstract

In a previous work we introduced Dual Light Affine Logic (DLAL) ([BaillotTerui04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can be evaluated in polynomial time and all Ptime functions can be represented. In the present work we address the problem of typing lambda-terms in second-order DLAL. For that we give a procedure which, starting with a term typed in system F, finds all possible ways to decorate it into a DLAL typed term. We show that our procedure can be run in time polynomial in the size of the original Church typed system F term.