What's decidable about weighted automata?

Shaull Almagor*, Udi Boker, Orna Kupferman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Weighted automata map input words to values, and have numerous applications in computer science. A result by Krob from the 90s implies that the universality problem is decidable for weighted automata over the tropical semiring with weights in N∪{∞} and is undecidable when the weights are in Z∪{∞}. We continue the study of the borders of decidability in weighted automata over the tropical semiring. We give a complete picture of the decidability and complexity of various decision problems for them, including non-emptiness, universality, equality, and containment. For the undecidability results, we provide direct proofs, which stay in the terrain of state machines. This enables us to tighten the results and apply them to a very simple class of automata. In addition, we provide a toolbox of algorithms and techniques for weighted automata, on top of which we establish the complexity bounds.

Original languageAmerican English
Article number104651
Pages (from-to)1-20
Number of pages20
JournalInformation and Computation
StatePublished - Jan 2022

Bibliographical note

Funding Information:
S. Almagor has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk?odowska-Curie grant agreement No. 837327. U. Boker is funded by Israel Science Foundation grant 1373/16. O. Kupferman was supported in part by the Israel Science Foundation, grant No. 2357/19.

Publisher Copyright:
© 2020 Elsevier Inc.


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