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On Quasi-Interpretations, Blind Abstractions and Implicit Complexity

Patrick Baillot·Ugo Dal Lago·Jean-Yves Moyen
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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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Patrick Baillot, Ugo Dal Lago, Jean-Yves Moyen. 2006-08-06. On Quasi-Interpretations, Blind Abstractions and Implicit Complexity. https://arxiv.org/abs/cs/0608030

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