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On quasi-interpretations, blind abstractions and implicit complexity.

Patrick Baillot 1 Ugo Dal Lago 2, 3 Jean-Yves Moyen 4
3 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
4 LCR - Logic, Computation and Reasoning [Villetaneuse]
LIPN - Laboratoire d'Informatique de Paris-Nord
Abstract : Quasi-interpretations are a technique for guaranteeing complexity bounds on first-order functional programs: in particular, with termination orderings, they give a sufficient condition for a program to be executable in polynomial time (Marion and Moyen 2000), which we call the P-criterion here. We study properties of the programs satisfying the P-criterion in order to improve the understanding of its intensional expressive power. Given a program, its blind abstraction is the non-deterministic program obtained by replacing all constructors with the same arity by a single one. A program is blindly polytime if its blind abstraction terminates in polynomial time. We show that all programs satisfying a variant of the P-criterion are in fact blindly polytime. Then we give two extensions of the P-criterion: one relaxing the termination ordering condition and the other (the bounded-value property) giving a necessary and sufficient condition for a program to be polynomial time executable, with memoisation.
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Submitted on : Friday, March 8, 2013 - 2:32:55 PM
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Patrick Baillot, Ugo Dal Lago, Jean-Yves Moyen. On quasi-interpretations, blind abstractions and implicit complexity.. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2012, 22 (04), pp.549-580. ⟨10.1017/S0960129511000685⟩. ⟨hal-00798377⟩



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