Bell, PC ORCID: https://orcid.org/0000-0003-2620-635X, Chen, S and Jackson, L (2019) Freeness properties of weighted and probabilistic automata over bounded languages. Information and Computation, 269 (104440). -.

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Abstract

There has been much research into freeness properties of finitely generated matrix semigroups under various constraints, such as the dimensions of the generator matrices and the semiring over which the matrices are defined. Most freeness problems have been shown to be undecidable starting from dimension three, even for upper-triangular matrices over the natural numbers. There are many open problems still remaining in dimension two. A recent paper has also investigated freeness properties of bounded languages of matrices, which are matrices from a set M∗1 M∗2· · · M∗k ⊆ Fn×n for some semiring F and a fixed value k ∈ N>0, where matrices M1, . . . , Mk are given [1]. We consider a notion of freeness and ambiguity for scalar reachability problems in matrix semigroups and bounded languages of matrices. Scalar reachability concerns the set {ρTMτ |M ∈ S}, where ρ, τ ∈ F n are vectors and S ⊆ F n×n is a finitely generated matrix semigroup. Ambiguity and freeness problems are defined in terms of the uniqueness of factorizations for each scalar. Such problems have also been studied in connection to formal power series. We show various undecidability results and their connections to weighted and probabilistic finite automata.

Item Type: Article
Additional Information: The final version of this accepted manuscript and all relevant information related to it, including copyrights, can be found on the publisher website.
Subjects: Q Science > QA Mathematics
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 25 Jul 2022 15:02
Last Modified: 25 Jul 2022 15:02
URI: https://eprints.keele.ac.uk/id/eprint/11109

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