Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition

Yan, Yongyi; Chen, Zengqiang; Liu, Zhongxin

doi:10.1007/s11704-014-3425-y

Cited by 28 publications

(12 citation statements)

References 20 publications

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“…Subsequently, considering the vector forms of finite automata, by resorting to Theorem 3 and STP method, some interesting problems, including reachability, observability, controllability and stabilization, were studied [141,143,144,174,175]. In detail, Xu et al [141] proposed a necessary and sufficient condition for reachability of finite automata by using the introduced matrix-based approach, from which the vector form of the required input string can be easily constructed.…”

Section: Definition 2 ([174])mentioning

confidence: 99%

“…The main advantage is that this method can be performed uniformly for analyzing reachability of deterministic and nondeterministic automata. Then in [143], reachability of finite automata was reconsidered with its application to language recognition, and an algorithm was designed to discover all the paths between two states. Xu and Hong [175] uniformly analyzed observability of partial observed non-deterministic automata either with or without input information by the matrix expression method, and also established a constructive algorithm to design the required observers.…”

Section: Definition 2 ([174])mentioning

confidence: 99%

“…On the other hand, STP method has wide applications in the engineering related field. These applications include gene regulation [124,125], power system [126][127][128][129], wireless communication [130][131][132], smart grid [133][134][135][136][137][138][139], finite automata [140][141][142][143][144], information security [145][146][147], vehicle control [148][149][150], indoor thermal comfort [151][152][153][154], fault detection of circuits [155,156], spacecraft [157], epidemic vaccination [158], mobile robot [159]. The aim of this paper is to present a comprehensive survey on these applications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A survey on applications of semi-tensor product method in engineering

Zhao

Meng

et al. 2017

Sci. China Inf. Sci.

107

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Semi-tensor product (STP) of matrices has attracted more and more attention from both control theory and engineering in the last two decades. This paper presents a comprehensive survey on the applications of STP method in engineering. Firstly, some preliminary results on STP method are recalled. Secondly, some applications of STP method in engineering, including gene regulation, power system, wireless communication, smart grid, information security, combustion engine and vehicle control, are reviewed. Finally, some potential applications of STP method are predicted.

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Section: Definition 2 ([174])mentioning

confidence: 99%

Section: Definition 2 ([174])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A survey on applications of semi-tensor product method in engineering

Zhao

Meng

et al. 2017

Sci. China Inf. Sci.

107

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“…The STP method has also been successfully used to investigate networked evolutionary games, and many excellent works are obtained [19]- [22]. It's worth noting that STP is a powerful tool to study the mapping on finite sets [23], and it has been applied to many other fields, including Boolean networks [24]- [28], cooperative games [29], multi-valued logical systems [30], [31], power system [32], [33], finite automata [34], [35] and so on. Particularly, [36] give a comprehensive introduction to the engineering application of STP approach.…”

Section: Introductionmentioning

confidence: 99%

Weighted Potential Incomplete-Profile Games

Pan

Zhao

2020

IEEE Access

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In this paper the weighted potential incomplete-profile games are studied. First a potential equation with algebraic form is established to check whether an incomplete-profile normal form game (IPNFG) is a weighted potential game with weight w > 0 or not, based on which, the potential function can be constructed. Then the weighted potential subspace and the non-strategic subspace and some properties of weighted potential incomplete-profile games are obtained. Finally, an example is given to illustrate our theoretical results. INDEX TERMS Incomplete-profile games, weighted potential subspace, non-strategic subspace, semitensor product of matrices.

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“…The algebraic approach is an elegant way to construct and analyze finite automata. The theory of STP which was proposed by Cheng , is a new powerful matrix analysis method and tool.…”

Section: Introductionmentioning

confidence: 99%

STP Approach to Model Controlled Automata with Application to Reachability Analysis of DEDS

Yan

Chen

Yue

et al. 2016

Asian Journal of Control

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This paper introduces semi-tensor product of matrices (STP), a new matrix analysis tool, into the field of discrete event dynamic system (DEDS). Using STP, the dynamics of controlled automaton are modelled as an algebraic expression of the states, events and control specification. Based on this algebraic description, a sufficient and necessary condition is proposed to check whether any two states of a DEDS are reachable or not. The condition suggests an algorithm which can discover all the event strings by which a controlled automaton can move to one state from another one if they are reachable. All the results can be used to analyze corresponding problems of finite automata after simple modification. Finally, illustrative examples examine the correctness of the presented results/algorithm and demonstrate the modification after which the results are suitable for finite automata. The approach of this paper provides a new angle and means to understand and analyze the dynamics of DEDS.

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Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition

Cited by 28 publications

References 20 publications

A survey on applications of semi-tensor product method in engineering

A survey on applications of semi-tensor product method in engineering

Weighted Potential Incomplete-Profile Games

STP Approach to Model Controlled Automata with Application to Reachability Analysis of DEDS

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