eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-03-12
43:1
43:13
10.4230/LIPIcs.STACS.2019.43
article
On Finite Monoids over Nonnegative Integer Matrices and Short Killing Words
Kiefer, Stefan
1
Mascle, Corto
2
University of Oxford, UK
ENS Paris-Saclay, France
Let n be a natural number and M a set of n x n-matrices over the nonnegative integers such that M generates a finite multiplicative monoid. We show that if the zero matrix 0 is a product of matrices in M, then there are M_1, ..., M_{n^5} in M with M_1 *s M_{n^5} = 0. This result has applications in automata theory and the theory of codes. Specifically, if X subset Sigma^* is a finite incomplete code, then there exists a word w in Sigma^* of length polynomial in sum_{x in X} |x| such that w is not a factor of any word in X^*. This proves a weak version of Restivo’s conjecture.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol126-stacs2019/LIPIcs.STACS.2019.43/LIPIcs.STACS.2019.43.pdf
matrix semigroups
unambiguous automata
codes
Restivo’s conjecture