arXiv subjects

Zhengfeng Yang

Publications and source records attributed to Zhengfeng Yang.

21 records · Page 2Linked to original sources

arXiv2012

Exact Safety Verification of Hybrid Systems Based on Bilinear SOS Representation

In this paper, we address the problem of safety verification of nonlinear hybrid systems. A hybrid symbolic-numeric method is presented to compute exact inequality invariants of hybrid systems efficiently. Some numerical invariants of a hybrid system can be obtained by solving a bilinear SOS programming via PENBMI solver or iterative method, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact polynomial invariants with rational coefficients, which {\it exactly} satisfy the conditions of invariants. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.

cs.SE↗

arXiv2011

Exact Safety Verification of Hybrid Systems Using Sums-Of-Squares Representation

In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems. A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems. A numerical invariant of the given system can be obtained by solving a parameterized polynomial optimization problem via sum-of-squares (SOS) relaxation. And a method based on Gauss-Newton refinement and rational vector recovery is deployed to obtain the invariants with rational coefficients, which exactly satisfy the conditions of invariants. Several examples are given to illustrate our algorithm.

cs.SE↗

arXiv2011

Generating Loop Invariants by Computing Vanishing Ideals of Sample Points

Loop invariants play a very important role in proving correctness of programs. In this paper, we address the problem of generating invariants of polynomial loop programs. We present a new approach, for generating polynomial equation invariants of polynomial loop programs through computing vanishing ideals of sample points. We apply rational function interpolation, based on early termination technique, to generate invariants of loop programs with symbolic initial values. Our approach avoids first-order quantifier elimination and cylindrical algebraic decomposition(CAD). An algorithm for generating polynomial invariants is proposed and some examples are given to illustrate the algorithm. Furthermore, we demonstrate on a set of loop programs with symbolic initial values that our algorithm can yield polynomial invariants with degrees high up to 15.

cs.SC↗