TY - GEN

T1 - Stochastization of weighted automata

AU - Avni, Guy

AU - Kupferman, Orna

N1 - Funding Information: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no 278410, and from The Israel Science Foundation (grant no 1229/10). Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84943591888&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-662-48057-1_7

DO - https://doi.org/10.1007/978-3-662-48057-1_7

M3 - Conference contribution

SN - 9783662480564

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 89

EP - 102

BT - Mathematical Foundations of Computer Science 2015 - 40th International Symposium, MFCS 2015, Proceedings

A2 - Pighizzini, Giovanni

A2 - Italiano, Giuseppe F.

A2 - Sannella, Donald T.

PB - Springer Verlag

T2 - 40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015

Y2 - 24 August 2015 through 28 August 2015

ER -