Approximate Completed Trace Equivalence of Linear Algebra Transition Systems

Yang, Hao; He, Anping; Zhang, Zhiwei; Yang, Shihan; Liu, Yang

doi:10.1007/978-3-642-37502-6_29

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…Generating the invariant by polynomials Gröebner base is proposed firstly in hybrid system in 2004 [8]. Then the variables refinement and equivalences were proposed [9][10][11][12]. But in differential semi-algebra system, the refinement has not been concerned, so we study the refinement in differential semi-algebra systems that contain differential and semi-algebra.…”

Section: Introductionmentioning

confidence: 99%

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Equivalences in Variables Refinement for Differential Semi-algebraic Hybrid Systems

Liu

Wang

Nie

2022

J. Phys.: Conf. Ser.

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Differential semi-algebra hybrid system is a new formalized hybrid system model; it is widely used in engineering technology. In this paper we proposed differential semi-algebraic event structure as the system model, and then build the variables refinement theory of differential semi-algebraic hybrid system. Based on the various equivalence relationship, we researched the keeping equivalence after variables refinement.

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Section: Introductionmentioning

confidence: 99%

“…After variables refinement，research the equivalence preservation problem. In the paper we proposed trace equivalence and bisimulation equivalence which is discussed in literature [9,10,13,20]. Then we find which equivalences are kept after the variables refinement.…”

Section: Introductionmentioning

confidence: 99%

Equivalences in Variables Refinement for Differential Semi-algebraic Hybrid Systems

Liu

Wang

Nie

2022

J. Phys.: Conf. Ser.

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“…The paper [13] firstly used polynomial equation to define the state transition hybrid system, and through polynomials Groebner base generate the invariant. Based on these, some equivalence and approximate equivalence were proposed [14,15,16]. But the refinement of hybrid system is not mentioned.…”

Section: Introductionmentioning

confidence: 99%

Approximate Bisimulation Equivalence and Variable Refinement

Liu¹,

Wu²,

Xie³

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper, we consider an operator for refinement of variables to be used in the design of hybrid system. Variables on a given level of abstraction are replaced by more complicated processes on a lower level just like the function are called in the program. Then we established the equivalence, bisimulation equivalence and approximate bisimulation equivalence which are by polynomial flow event structures. These equivalence, bisimulation equivalence and approximate bisimulation equivalence are based on the common forms of their zeros. The example show that the equivalence, bisimulation equivalence and approximate bisimulation equivalence are preserved or not under the variables refinement, if the equivalence is not preserved precisely, then we can use the approximate methods to make them approximate equivalence. Lastly we show that our refinement has some nice properties.

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Variable refinement on semi-algebraic flow event structure

Liu

Zou

2017

2017 8th IEEE International Conference on Software Engineering and Service Science (ICSESS)

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Approximate Completed Trace Equivalence of Linear Algebra Transition Systems

Cited by 3 publications

References 6 publications

Equivalences in Variables Refinement for Differential Semi-algebraic Hybrid Systems

Equivalences in Variables Refinement for Differential Semi-algebraic Hybrid Systems

Approximate Bisimulation Equivalence and Variable Refinement

Variable refinement on semi-algebraic flow event structure

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