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Open AccessArticle

Approximate Completed Trace Equivalence of ILAHSs Based on SAS Solving

by Honghui He 1,2,3,4, Jinzhao Wu 1,2,3,* and Juxia Xiong 1,2,3
1
Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China
2
University of Chinese Academy of Sciences, Beijing 100049, China
3
Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China
4
School of Computer Software, Henan University, Kaifeng 475001, China
*
Author to whom correspondence should be addressed.
Information 2019, 10(11), 340; https://doi.org/10.3390/info10110340
Received: 6 September 2019 / Revised: 21 October 2019 / Accepted: 23 October 2019 / Published: 1 November 2019
The ILAHS (inhomogeneous linear algebraic hybrid system) is a kind of classic hybrid system. For the purpose of optimizing the design of ILAHS, one important strategy is to introduce equivalence to reduce the states. Recent advances in the hybrid system indicate that approximate trace equivalence can further simplify the design of ILAHS. To address this issue, the paper first introduces the trajectory metric d t r j for measuring the deviation of two hybrid systems’ behaviors. Given a deviation ε 0 , the original ILAHS of H 1 can be transformed to the approximate ILAHS of H 2 , then in trace equivalence semantics, H 2 is further reduced to H 3 with the same functions, and hence H 1 is ε -approximate trace equivalent to H 3 . In particular, ε = 0 is a traditional trace equivalence. We implement an approach based on RealRootClassification to determine the approximation between the ILAHSs. The paper also shows that the existing approaches are only special cases of our method. Finally, we illustrate the effectiveness and practicality of our method on an example. View Full-Text
Keywords: approximate equivalence; hybrid system; inhomogeneous linear algebraic hybrid systems; RealRootClassification approximate equivalence; hybrid system; inhomogeneous linear algebraic hybrid systems; RealRootClassification
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He, H.; Wu, J.; Xiong, J. Approximate Completed Trace Equivalence of ILAHSs Based on SAS Solving. Information 2019, 10, 340.

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