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On quasi-interpretations, blind abstractions and implicit complexity†

Published online by Cambridge University Press:  02 February 2012

PATRICK BAILLOT ,
UGO DAL LAGO  and
JEAN-YVES MOYEN
PATRICK BAILLOT
Affiliation:
LIP, UMR 5668 CNRS, ENS-Lyon, UCBL, INRIA, Université de Lyon, France Email: patrick.baillot@ens-lyon.fr
UGO DAL LAGO
Affiliation:
Università di Bologna, Italy Email: dallago@cs.unibo.it
JEAN-YVES MOYEN
Affiliation:
LIPN, UMR 7030 CNRS, Université Paris 13, France Email: jean-yves.moyen@lipn.univ-paris13.fr
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Issue 4 , August 2012 , pp. 549 - 580
Copyright
Copyright © Cambridge University Press 2012

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