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On Quasi-Interpretations, Blind Abstractions and Implicit Complexity

Authors
  • Baillot, Patrick
  • Lago, Ugo Dal
  • Moyen, Jean-Yves
Type
Preprint
Publication Date
Aug 06, 2006
Submission Date
Aug 06, 2006
Identifiers
arXiv ID: cs/0608030
Source
arXiv
License
Unknown
External links

Abstract

Quasi-interpretations are a technique to guarantee complexity bounds on first-order functional programs: with termination orderings they give in particular a sufficient condition for a program to be executable in polynomial time, called here the P-criterion. We study properties of the programs satisfying the P-criterion, in order to better understand its intensional expressive power. Given a program on binary lists, its blind abstraction is the nondeterministic program obtained by replacing lists by their lengths (natural numbers). A program is blindly polynomial if its blind abstraction terminates in polynomial time. We show that all programs satisfying a variant of the P-criterion are in fact blindly polynomial. Then we give two extensions of the P-criterion: one by relaxing the termination ordering condition, and the other one (the bounded value property) giving a necessary and sufficient condition for a program to be polynomial time executable, with memoisation.

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