On Sharing, Memoization, and Polynomial Time
Proceedings of the 32nd International Symposium on Theoretical Aspects of Computer Science, volume 30 of Leibnitz International Proceedings in Informatics, pages 62–75, 2015.
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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 result 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.