Analysing Parallel Complexity of Term Rewriting

TL;DR

This paper explores the parallel complexity of term rewriting, introducing methods to automatically derive bounds and demonstrating their effectiveness through tool extension and benchmark experiments.

Contribution

It presents a new approach to analyze parallel complexity in term rewriting, enabling reuse of existing sequential complexity techniques.

Findings

Effective bounds on parallel complexity derived

Successful extension of AProVE tool demonstrated

Experimental validation on multiple benchmarks

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. 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.