On Complexity Bounds and Confluence of Parallel Term Rewriting
Abstract
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. Our approach to find lower bounds requires confluence of the parallel-innermost rewrite relation, thus we also provide effective sufficient criteria for proving confluence. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature.
Cite
@article{arxiv.2305.18250,
title = {On Complexity Bounds and Confluence of Parallel Term Rewriting},
author = {Thaïs Baudon and Carsten Fuhs and Laure Gonnord},
journal= {arXiv preprint arXiv:2305.18250},
year = {2026}
}
Comments
Final version formatted by the editorial board. Accepted for publication in Fundamenta Informaticae, special issue for LOPSTR 2022. arXiv admin note: substantial text overlap with arXiv:2208.01005