On sharing, memoization, and polynomial time

Martin Avanzini (1) , Ugo Dal Lago (2, 1)

1 FOCUS - Foundations of Component-based Ubiquitous Systems
2 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna

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.

Domaines: Langage de programmation [cs.PL]; Logique en informatique [cs.LO]

Martin Avanzini, Ugo Dal Lago. On sharing, memoization, and polynomial time. Information and Computation, 2018, 261, pp.3 - 22. ⟨10.1016/j.ic.2018.05.003⟩. ⟨hal-01926431⟩