On Sharing, Memoization, and Polynomial Time

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


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.


ICC, Predicative Recursion, Invariance