LAL is square: Representation and expressiveness in light affine logic (2002)
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| Venue: | In Proc. Workshop on Implicit Computational Complexity |
| Citations: | 3 - 2 self |
BibTeX
@INPROCEEDINGS{Neergaard02lalis,
author = {Peter Møller Neergaard and Harry G. Mairson},
title = {LAL is square: Representation and expressiveness in light affine logic},
booktitle = {In Proc. Workshop on Implicit Computational Complexity},
year = {2002}
}
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Abstract
Abstract. We focus on how the choice of input-output representation has a crucial impact on the expressiveness of so-called “logics of polynomial time. ” Our analysis illustrates this dependence in the context of Light Affine Logic (LAL), which is both a restricted version of Linear Logic, and a primitive functional programming language with restricted sharing of arguments. By slightly relaxing representation conventions, we derive doubly-exponential expressiveness bounds for this “logic of polynomial time. ” We emphasize that squaring is the unifying idea that relates upper bounds on cut elimination for LAL with lower bounds on representation. Representation issues arise in the simulation of DTIME[2 2n], where we construct a uniform family of proof-nets encoding a Turing Machine; specifically, the dependence on n only affects the number of enclosing boxes. A related technical improvement is the simulation of DTIME[n k]indepthO(log k) LAL proof-nets. The resulting upper bounds on cut elimination then satisfy the properties of a
