A POLYNOMIAL TIME ALGORITHM FOR COMPUTING EXTINCTION PROBABILITIES OF MULTITYPE BRANCHING PROCESSES

被引：1
|
作者：
Etessami, Kousha [1 ]
Stewart, Alistair [2 ]
Yannakakis, Mihalis [3 ]
机构：
[1] Univ Edinburgh, Sch Informat, Edinburgh EH8 9AB, Midlothian, Scotland
[2] Univ Southern Calif, Dept Comp Sci, Los Angeles, CA 90007 USA
[3] Columbia Univ, Dept Comp Sci, New York, NY 10027 USA
来源：
SIAM JOURNAL ON COMPUTING | 2017年 / 46卷 / 05期
关键词：
multitype branching processes; extinction probabilities; polynomial time algorithms; nonlinear systems of equations; Newton's method; computational complexity; COMPLEXITY; TREE;
D O I：
10.1137/16M105678X
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
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/c), where c > 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 well studied stochastic processes, including multitype branching processes and stochastic context-free grammars.
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页码：1515 / 1553
页数：39
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