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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 421926, 19 pages
Research Article

Approximate Bisimulation and Optimization of Software Programs Based on Symbolic-Numeric Computation

1School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China
2Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, Guangxi 530006, China

Received 9 April 2013; Revised 6 August 2013; Accepted 7 August 2013

Academic Editor: Yang Xu

Copyright © 2013 Hui Deng and Jinzhao Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


To achieve behavior and structure optimization for a type of software program whose data exchange processes are represented by nonlinear polynomial systems, this paper establishes a novel formal description called a nonlinear polynomial transition system to represent the behavior and structure of the software program. Then, the notion of bisimulation for software programs is proposed based on the equivalence relation of corresponding nonlinear polynomial systems in their nonlinear polynomial transition systems. However, the exact equivalence is too strict in application. To enhance the flexibility of the relation among the different software systems, the notion of approximate bisimulation within a controllable error range and the calculation algorithm of approximate bisimulation based on symbolic-numeric computation are given. In this calculation, an approximate relation is represented as a MAX function that is resolved with the full filled method. At the same time, the actual error is calculable. An example on a multithreading program indicates that the approximate bisimulation relation is feasible and effective in behavior and structure optimization.