文章基本信息
- 标题：On LTL Model Checking for Low-Dimensional Discrete Linear Dynamical Systems
- 本地全文：下载
- 作者：Toghrul Karimov ; Jo{"e}l Ouaknine ; James Worrell 等
- 期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
- 电子版ISSN：1868-8969
- 出版年度：2020
- 卷号：170
- 页码：54:1-54:14
- DOI：10.4230/LIPIcs.MFCS.2020.54
- 出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
- 摘要：Consider a discrete dynamical system given by a square matrix M â^^ â"S^{d Ã- d} and a starting point s â^^ â"S^d. The orbit of such a system is the infinite trajectory âY¨ s, Ms, M²s, â¦âY©. Given a collection Tâ,, Tâ,,, â¦, T_m âS â"^d of semialgebraic sets, we can associate with each T_i an atomic proposition P_i which evaluates to true at time n if, and only if, M^ns â^^ T_i. This gives rise to the LTL Model-Checking Problem for discrete linear dynamical systems: given such a system (M,s) and an LTL formula over such atomic propositions, determine whether the orbit satisfies the formula. The main contribution of the present paper is to show that the LTL Model-Checking Problem for discrete linear dynamical systems is decidable in dimension 3 or less.
- 关键词：Linear dynamical systems; Orbit Problem; LTL model checking
