Affiliations: [a] LIP (UMR CNRS/ENS Lyon/UCB Lyon1/Inria), Lyon, France
| [b] Birkbeck, University of London, London, United Kingdom
| [c] LCIS, University Grenoble Alpes, Valence, France
Correspondence:
[†]
Address for correspondence: Birkbeck, University of London, London, United Kingdom.
Note: [*] This work was partially funded by the French National Agency of Research in the CODAS Project (ANR-17-CE23-0004-01). For Open Access purposes, our extended authors’ accepted manuscript [1] of this paper is available under Creative Commons CC BY licence.
Note: [‡] Also work: LIP (UMR CNRS/ENS Lyon/UCB Lyon1/Inria), Lyon, France.
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.
Keywords: Term rewriting, confluence, complexity analysis, parallelism, static analysis
