多类型分支过程和随机上下文无关文法的多项式时间算法
Polynomial Time Algorithms for Multi-Type Branching Processes and Stochastic Context-Free Grammars
摘要：
我们证明了一个多元单调概率多项式方程组的最小不动点解在时间多项式中可以在方程组的编码大小和log（1/ε）中逼近，其中ε> 0是解的期望加性误差界. (The计算模型是标准的图灵机模型。）我们使用这个结果来解决几个开放的问题，计算与一些经典的和大量研究的随机过程，包括多类型的分支过程和随机上下文无关文法的关键量的计算复杂性。
英文摘要：
We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/ε), where ε> 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open problems regarding the computational complexity of computing key quantities associated with some classic and heavily studied stochastic processes, including multi-type branching processes and stochastic context-free grammars.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
