## 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 language | American English |
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Title of host publication | Mathematical Foundations of Computer Science 2015 - 40th International Symposium, MFCS 2015, Proceedings |

Editors | Giovanni Pighizzini, Giuseppe F. Italiano, Donald T. Sannella |

Publisher | Springer Verlag |

Pages | 89-102 |

Number of pages | 14 |

ISBN (Print) | 9783662480564 |

DOIs | |

State | Published - 2015 |

Event | 40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015 - Milan, Italy Duration: 24 Aug 2015 → 28 Aug 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9234 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015 |
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Country/Territory | Italy |

City | Milan |

Period | 24/08/15 → 28/08/15 |

### Bibliographical note

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.