Stochastization of weighted automata

Guy Avni*, Orna Kupferman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

Nondeterministic weighted finite automata (WFAs) map input words to real numbers. Each transition of a WFA is labeled by both a letter from some alphabet and a weight. The weight of a run is the sum of the weights on the transitions it traverses, and the weight of a word is the minimal weight of a run on it. In probabilistic weighted automata (PWFAs), the transitions are further labeled by probabilities, and the weight of a word is the expected weight of a run on it. We define and study stochastization of WFAs: given a WFA A, stochastiza-tion turns it into a PWFA A′ by labeling its transitions by probabilities. The weight of a word in A′ can only increase with respect to its weight in A, and we seek stochastizations in which A′ α-approximates A for the minimal possible factor a α; 1. That is, the weight of every word in A′ is at most a times its weight in A. We show that stochastization is useful in reasoning about the competitive ratio of randomized online algorithms and in approximated determinization of WFAs. We study the problem of deciding, given a WFA A and a factor α ≥ 1, whether there is a stochastization of A that achieves an α-approximation. We show that the problem is in general undecidable, yet can be solved in PSPACE for a useful class of WFAs.

Original languageAmerican English
Title of host publicationMathematical Foundations of Computer Science 2015 - 40th International Symposium, MFCS 2015, Proceedings
EditorsGiovanni Pighizzini, Giuseppe F. Italiano, Donald T. Sannella
PublisherSpringer Verlag
Pages89-102
Number of pages14
ISBN (Print)9783662480564
DOIs
StatePublished - 2015
Event40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015 - Milan, Italy
Duration: 24 Aug 201528 Aug 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9234
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015
Country/TerritoryItaly
CityMilan
Period24/08/1528/08/15

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

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