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On sharing, memoization, and polynomial time

On sharing, memoization, and polynomial time
Martin Avanzini and Ugo Dal Lago
Inf. Comput. 261: 3–22 (2018)

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.

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