吉林大学学报(工学版) ›› 2013, Vol. 43 ›› Issue (04): 1052-1058.doi: 10.7964/jdxbgxb201304033

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Approximate bisimulation for linear semi-algebraic transition systems

DENG Hui1, WU Jin-zhao2   

  1. 1. School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China;
    2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China
  • Received:2012-03-27 Online:2013-07-01 Published:2013-07-01

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Abstract:

As the transitions of states for software program have inequality constraints, a formal description, named linear semi-algebraic transition system, is proposed for program. With using characteristic set, a novel notion of bisimulation is established to simplify the structure of programs on the basis of common zeros of linear semi-algebraic systems. However, in applications, most of experimental data only have approximate values within an given error range. Therefore, the exact equivalence relations lack fault tolerance and flexibility. To obtain more appropriate relations for software programs, Singular Value Decomposition (SVD) is used to approximately process the systems and achieve the notion and calculation of approximate bisimulation. By symbolic and numerical hybrid computation, the error is computed and controlled. Finally, the approximate system is used to replace the original complex system. A case analysis of concurrent communication program shows that our approach is reasonable and effective for simplifying software program design.

Key words: computer software, approximate bisimulation, linear semi-algebraic transition systems, characteristic set, singular value decomposition, concurrent communication program

CLC Number: 

  • TP301

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