We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity in the model of Massively Parallel Computation, where $N$ is the input size. We show that if the machines are not equipped with relatively large local memory and their number does not exceed $N$, then the exponent of the average time complexity of the local computation performed by a machine in a round (in terms of local memory size) in such protocols must be larger than the exponent of the time complexity of the given problem.

翻译：我们研究在巨量并行计算模型中为具有大幅超线性多项式时间（顺序）复杂性问题设计$N^{o(1)}$轮协议的可能性，其中$N$为输入规模。研究表明：若机器未配备相对较大的局部内存且其数量不超过$N$，则在此类协议中，单台机器在一轮内执行的局部计算的平均时间复杂度指数（以局部内存大小为度量）必须大于给定问题的时间复杂度指数。