Abstract
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 language | English |
|---|---|
| Article number | 104651 |
| Pages (from-to) | 1-20 |
| Number of pages | 20 |
| Journal | Information and Computation |
| Volume | 282 |
| DOIs | |
| State | Published - 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.
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