main.pdf (300.28 kB)
Scalar ambiguity and freeness in matrix semigroups over bounded languages
conference contribution
posted on 2016-01-20, 13:47 authored by Paul Bell, Shang Chen, Lisa JacksonLisa JacksonThere 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.
History
School
- Science
Department
- Computer Science
Published in
Language and Automata Theory and Applications (LATA 2016)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.Publisher
© Springer VerlagVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2016Notes
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_38ISSN
0302-9743Publisher version
Language
- en