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.

翻译：本文重新审视了并行最内项重写作为归纳数据结构上并行计算模型的特性，并提出了基于起始项规模的运行时复杂度参数化概念。我们提出了自动推导重写并行复杂度上下界的技术，该技术能够直接复用现有的串行复杂度分析方法。我们寻找下界的方法要求并行最内重写关系具有合流性，因此本文同时提供了证明合流性的有效充分条件。通过以相对较小的代价扩展程序分析工具AProVE，并结合文献中大量基准测试的实验结果，验证了该方法的适用性与精确性。