REACH swMATH ID: 7733 Software Authors: Xu, Ming; Zhu, Jiaqi; Li, Zhi-Bin Description: Some decidable results on reachability of solvable systems Reachability analysis plays an important role in verifying the safety of modern control systems. In the existing work, there are many decidable results on reachability of discrete systems. For continuous systems, however, the known decidable results are established merely for linear systems. In this paper, we propose a class of nonlinear systems (named solvable systems) extending linear systems. We first show that their solutions are of closed form. On the basis of it, we study a series of reachability problems for various subclasses of solvable systems. Our main results are that these reachability problems are decidable by manipulations in number theory, real root isolation, and quantifier elimination. Finally the decision procedures are implemented in a Maple package REACH to solve several non-trivial examples. Homepage: http://www.tandfonline.com/doi/abs/10.1080/03081079.2012.757604#.UtONLFu0UYw Dependencies: Maple Keywords: reachability analysis; solvable mappings; nonlinear systems; hybrid systems; symbolic computation; decision procedures Related Software: iscasMc; z3; REDLOG; MRMC; PRISM; TERMINATOR; Maple; ISOLATE; QEPCAD Cited in: 4 Publications all top 5 Cited by 10 Authors 4 Xu, Ming 3 Li, Zhibin 2 Huang, Chengchao 1 Jansen, David N. 1 Li, Jing-Cao 1 Yang, Zongyuan 1 Zeng, Zhenbing 1 Zhang, Lijun 1 Zhu, Huibiao 1 Zhu, Jiaqi Cited in 3 Serials 2 Theoretical Computer Science 1 International Journal of General Systems 1 Journal of Symbolic Computation all top 5 Cited in 7 Fields 2 Computer science (68-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year