Abstract

We give a realizability model of Girard-Scedrov-Scott's Bounded Linear Logic (BLL). This gives a new proof that all numerical functions representable in that system are polytime. Our analysis naturally justifies the design of the BLL syntax and suggests further extensions. 1 Introduction Bounded Linear Logic (BLL) [3] was an early attempt to provide an intrinsic notion of polynomial time computation within a logical system. That is, the aim was not merely to express polynomial time computability in terms of provability of certain restricted formulas, but rather to provide a typed logical system in which computation via cut-elimination or proof normalization is inherently polytime. Since the appearance of this paper, several di#erent typed functional systems for analyzing ptime computability have appeared in the literature [5, 4, 10, 11, 6, 7]. For deeper foundational purposes, we should mention Girard's Light Linear Logic (LLL) [4] as a major improvement of the syntax of BLL, in that...

Citations