# What's Decidable about Weighted Automata?

@inproceedings{Almagor2011WhatsDA, title={What's Decidable about Weighted Automata?}, author={Shaull Almagor and Udi Boker and Orna Kupferman}, booktitle={ATVA}, year={2011} }

Weighted automata map input words to numerical values. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing.
In the 90's, Krob studied the decidability of problems on rational series, which strongly relate to weighted automata. In particular, it follows from Krob's results that the universality problem (that is, deciding whether the values of all words are below some threshold) is decidable for weighted…

## 86 Citations

The Big-O Problem for Labelled Markov Chains and Weighted Automata

- Computer Science, MathematicsCONCUR
- 2020

The positive results show that the big-O problem is polynomial-time solvable for unambiguous automata, coNP-complete for unlabelled weighted automata and decidable, subject to Schanuel's conjecture, when the language is bounded.

Rigorous approximated determinization of weighted automata

- Computer ScienceTheor. Comput. Sci.
- 2013

When are emptiness and containment decidable for probabilistic automata?

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 2021

Approximate Determinization of Quantitative Automata

- Computer ScienceFSTTCS
- 2012

This work defines approximate determinization with respect to a distance function, and provides an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states, and proves matching lower bounds, showing exponential dependency on each of these three parameters.

The Big-O Problem

- Computer Science, MathematicsLog. Methods Comput. Sci.
- 2022

The positive results show that the big-O problem is polynomial-time solvable for unambiguous automata, coNP-complete for unlabelled weighted automata and decidable, subject to Schanuel's conjecture, when the language is bounded.

Nested Weighted Automata

- Computer Science2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015

An almost complete decidability picture for the basic decision problems about nested weighted automata is established, and their applicability in several domains is illustrated, including average response time properties.

Nested Weighted Automata

- Computer ScienceLICS 2015
- 2015

An almost complete decidability picture for the basic decision problems about nested weighted automata is established, and their applicability in several domains is illustrated, including average response time properties.

364 Approximate Determinization of Quantitative Automata

- Computer Science
- 2012

This work defines approximate determinization with respect to a distance function, and provides an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states, and proves matching lower bounds, showing exponential dependency on each of these three parameters.

Quantitative Languages Defined by Functional Automata

- Computer Science, MathematicsCONCUR
- 2012

This paper investigates functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs, and shows that functionality is decidable for the four measures.

Regular Functions, Cost Register Automata, and Generalized Min-Cost Problems

- Computer ScienceArXiv
- 2011

A deterministic model for associating costs with strings that is parameterized by operations of interest, a notion of regularity that provides a yardstick to measure expressiveness, and study decision problems and theoretical properties of resulting classes of cost functions are proposed.

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