On Sharing, Memoization, and Polynomial Time (Long Version)
Computational Complexity
2015-01-06 v1
Abstract
We study how the adoption of an evaluation mechanism with sharing and memoization impacts the class of functions which can be computed in polynomial time. We first show how a natural cost model in which lookup for an already computed value has no cost is indeed invariant. As a corollary, we then prove that the most general notion of ramified recurrence is sound for polynomial time, this way settling an open problem in implicit computational complexity.
Cite
@article{arxiv.1501.00894,
title = {On Sharing, Memoization, and Polynomial Time (Long Version)},
author = {Martin Avanzini and Ugo Dal Lago},
journal= {arXiv preprint arXiv:1501.00894},
year = {2015}
}