On sharing, memoization, and polynomial time

Martin Avanzini 1 Ugo Dal Lago 2, 1
1 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
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.
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Submitted on : Monday, November 19, 2018 - 1:33:21 PM
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Martin Avanzini, Ugo Dal Lago. On sharing, memoization, and polynomial time. Information and Computation, Elsevier, 2018, 261, pp.3 - 22. ⟨10.1016/j.ic.2018.05.003⟩. ⟨hal-01926431⟩

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