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Title: Scalar ambiguity and freeness in matrix semigroups over bounded languages
Authors: Bell, Paul C.
Chen, Shang
Jackson, Lisa M.
Keywords: Matrix semigroup freeness
Scalar ambiguity
Bounded languages
Issue Date: 2016
Publisher: © Springer Verlag
Citation: BELL, P.C., CHEN, S. and JACKSON, L.M., 2016. Scalar ambiguity and freeness in matrix semigroups over bounded languages. Lecture Notes in Computer Science, 9618, pp.493-505.
Abstract: There has been much research into freeness properties of finitely generated matrix semigroups under various constraints, mainly related to the dimensions of the generator matrices and the semiring over which the matrices are defined. A recent paper has also investigated freeness properties of matrices within a bounded language of matrices, which are of the form M1M2 · · · Mk ⊆ F n×n for some semiring F [9]. 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. We introduce a notion of freeness and ambiguity for scalar reachability problems in matrix semigroups and bounded languages of matrices. Scalar reachability concerns the set {ρ TMτ |M ∈ S}, where ρ, τ ∈ F n are vectors and S is a finitely generated matrix semigroup. Ambiguity and freeness problems are defined in terms of uniqueness of factorizations leading to each scalar. We show various undecidability results.
Description: This paper was presented at LATA 2016: 10th International Conference on Language and Automata Theory and Applications http://grammars.grlmc.com/lata2016/. This is a pre‐copyedited version of a Lecture Notes in Computer Science published by Springer. The definitive authenticated version is available online via http://dx.doi.org/10.1007/978-3-319-30000-9_38
Version: Accepted for publication
DOI: 10.1007/978-3-319-30000-9_38
URI: https://dspace.lboro.ac.uk/2134/20094
Publisher Link: http://dx.doi.org/10.1007/978-3-319-30000-9_38
ISSN: 0302-9743
Appears in Collections:Conference Papers and Presentations (Computer Science)
Conference Papers and Presentations (Aeronautical and Automotive Engineering)

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