Let $n$ be a positive integer and $\mathcal M$ a set of rational $n \times n$-matrices such that $\mathcal M$ generates a finite multiplicative semigroup. We show that any matrix in the semigroup is a product of matrices in $\mathcal M$ whose length is at most $2^{n (2 n + 3)} g(n)^{n+1} \in 2^{O(n^2 \log n)}$, where $g(n)$ is the maximum order of finite groups over rational $n \times n$-matrices. This result implies algorithms with an elementary running time for deciding finiteness of weighted automata over the rationals and for deciding reachability in affine integer vector addition systems with states with the finite monoid property.

Article The effects of jitter on the peceptual quality of video Share on Authors: Mark Claypool Computer Science Department, Worcester Polytechnic Institute Computer Science Department, Worcester Polytechnic InstituteView Profile , Jonathan Tanner Computer Science Department, Worcester Polytechnic Institute Computer Science Department, Worcester Polytechnic InstituteView Profile Authors Info & Claims MULTIMEDIA '99: Proceedings of the seventh ACM international conference on Multimedia (Part 2)October 1999 Pages 115–118https://doi.org/10.1145/319878.319909Online:01 October 1999Publication History 78citation1,438DownloadsMetricsTotal Citations78Total Downloads1,438Last 12 Months70Last 6 weeks11 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access