On Quasi-Interpretations, Blind Abstractions and Implicit Complexity
<|reference_start|>On Quasi-Interpretations, Blind Abstractions and Implicit Complexity: 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.<|reference_end|>
@article{baillot2006on,
    title={On Quasi-Interpretations, Blind Abstractions and Implicit Complexity},
    author={Patrick Baillot, Ugo Dal Lago and Jean-Yves Moyen},
    journal={arXiv preprint arXiv:cs/0608030},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0608030},
    primaryClass={cs.PL cs.CC cs.LO}
}