Polynomial time algorithms for multi-type branching processesand stochastic context-free grammars

Authors:
Kousha Etessami;Alistair Stewart;Mihalis Yannakakis
Affiliations:
University of Edinburgh, Edinburgh, United Kingdom;School of Informatics, University of Edinburgh, United Kingdom;Columbia University, New York, NY, USA
Venue:
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Year:
2012

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Abstract

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 ε0 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.