Sciweavers

Share
QEST
2008
IEEE

Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems

9 years 4 months ago
Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems
We begin by observing that (discrete-time) QuasiBirth-Death Processes (QBDs) are equivalent, in a precise sense, to (discrete-time) probabilistic 1-Counter Automata (p1CAs), and both Tree-Like QBDs (TLQBDs) and Tree-Structured QBDs (TS-QBDs) are equivalent to both probabilistic Pushdown Systems (pPDSs) and Recursive Markov Chains (RMCs). We then proceed to exploit these connections to obtain a number of new algorithmic upper and lower bounds for central computational problems about these models. Our main result is this: for an arbitrary QBD (even a null-recurrent one), we can approximate its termination probabilities (i.e., its G matrix) to within i bits of precision (i.e., within additive error 1/2i ), in time polynomial in both the encoding size of the QBD and in i, in the unit-cost rational arithmetic RAM model of computation. Specifically, we show that a decomposed Newton’s method can be used to achieve this. We emphasize that this bound is very different from the well-known ...
Kousha Etessami, Dominik Wojtczak, Mihalis Yannaka
Added 01 Jun 2010
Updated 01 Jun 2010
Type Conference
Year 2008
Where QEST
Authors Kousha Etessami, Dominik Wojtczak, Mihalis Yannakakis
Comments (0)
books