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：我们重新审视并行最内层项重写，将其作为归纳数据结构上并行计算的模型，并相应提出了以起始项大小为参数的运行时复杂度概念。我们提出了自动推导重写并行复杂度的上下界技术，该技术能够直接复用现有顺序复杂度的分析方法。由于寻找下界的方法需要并行最内层重写关系满足合流性，我们还提供了证明合流性的有效充分条件。通过相对轻松地扩展程序分析工具AProVE，以及在大量文献基准上的实验，我们展示了该方法的适用性和精确性。