Polynomial Time Algorithms for Multi-Type Branching Processes and Stochastic Context-Free Grammars

Computer Science/Discrete Mathematics Seminar I
Topic:Polynomial Time Algorithms for Multi-Type Branching Processes and Stochastic Context-Free Grammars
Speaker:Mihalis Yannakakis
Affiliation:Columbia University
Date:Monday, November 14
Time/Room:11:15am - 12:15pm/S-101

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/epsilon), where epsilon > 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. (Joint work with Kousha Etessami and Alistair Stewart.)