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| Approximate Bisimulation and Its Applications for Polynomial Algebraic System Based on Symbolic and Numerical Calculation |
| Hui Deng, Jinzhao Wu |
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Abstract In this paper, a concept of approximate bisimulation is proposed by
symbolic computation for polynomial algebraic system and its
approximate abstraction based on the common forms of their zeros.
With using this idea for original system, on the one side, some
extra nondeterministic branches are removed to achieve structure
reduction. On the other hand, behavior reduction is achieved by
choosing simple expression to replace its complex approximate
equivalent expression. In addition, with symbolic and numerical
hybrid computation, the error caused by approximate definition is
computed and controlled. Based on our approach, the properties of
deadlock and safety are proved to be maintainable. Finally, the
results of the properties verification of simpler abstraction are
used to determine the results of the same properties for original
system. This method is applied to slow state explosion and decrease
computing effort. The application of our framework is demonstrated
on a program.
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