An Approximate Equivalence Based on process Algebra and Numerical Computation and for Differential Semi-algebraic Hybrid Systems

Abstract

In the paper, approximate ready trace equivalence for differential semi-algebraic hybrid system is proposed. The equivalence can be used to optimize differential semialgebraic hybrid system. The Concept is proposed on the basis of concrete process algebra and numerical analysis theory. In the approximate ready trace equivalence definition, we consider a cut operator for a polynomial and partial approximation for polynomial. Then we get a strict equivalence between two polynomials. Its advantage is that the new polynomial approximation method overcomes the drawback that traditional approximation method is not transitive, which can be used for automatic reasoning. In order to judge the two differential semi-algebraic hybrid system is equivalent, the axiom system for the approximate ready trace equivalence of differential semi-algebraic hybrid system is presented. This axiom system is a complete axiom system.