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DOI: 10.4230/LIPIcs.STACS.2010.2468
URN: urn:nbn:de:0030-drops-24685
URL: https://drops.dagstuhl.de/opus/volltexte/2010/2468/
Esparza, Javier ; Gaiser, Andreas ; Kiefer, Stefan
Computing Least Fixed Points of Probabilistic Systems of Polynomials
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Abstract
We study systems of equations of the form $X_1 = f_1(X_1, \ldots, X_n), \ldots, X_n = f_n(X_1, \ldots, X_n)$ where each $f_i$ is a polynomial with nonnegative coefficients that add up to~$1$. The least nonnegative solution, say~$\mu$, of such equation systems is central to problems from various areas, like physics, biology, computational linguistics and probabilistic program verification. We give a simple and strongly polynomial algorithm to decide whether $\mu=(1,\ldots,1)$ holds. Furthermore, we present an algorithm that computes reliable sequences of lower and upper bounds on~$\mu$, converging linearly to~$\mu$. Our algorithm has these features despite using inexact arithmetic for efficiency. We report on experiments that show the performance of our algorithms.
BibTeX - Entry
@InProceedings{esparza_et_al:LIPIcs:2010:2468,
author = {Javier Esparza and Andreas Gaiser and Stefan Kiefer},
title = {{Computing Least Fixed Points of Probabilistic Systems of Polynomials}},
booktitle = {27th International Symposium on Theoretical Aspects of Computer Science},
pages = {359--370},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-16-3},
ISSN = {1868-8969},
year = {2010},
volume = {5},
editor = {Jean-Yves Marion and Thomas Schwentick},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2010/2468},
URN = {urn:nbn:de:0030-drops-24685},
doi = {10.4230/LIPIcs.STACS.2010.2468},
annote = {Keywords: Computing fixed points, numerical approximation, stochastic models, branching processes}
}
| Keywords: | Computing fixed points, numerical approximation, stochastic models, branching processes | |
| Seminar: | 27th International Symposium on Theoretical Aspects of Computer Science | |
| Issue date: | 2010 | |
| Date of publication: | 09.03.2010 |
