Observability analysis of combined finite automata based upon semi-tensor product of matrices approach

2020 ◽  
pp. 014233122097252
Author(s):  
Zengqiang Chen ◽  
Yingrui Zhou ◽  
Zhipeng Zhang ◽  
Zhongxin Liu
Keyword(s):  
Tensor Product ◽  
Finite Automata ◽  
Initial State ◽  
Algebraic Form ◽  
Incidence Matrices ◽  
Observability Analysis ◽  
Current State ◽  
The Matrix ◽  
Problem Description ◽  
Product Of Matrices

As a fundamental subject, the state estimation of deterministic finite automata has received considerable attention. Especially, it is increasingly necessary to study various problems based on more complex systems. In this paper, the observability of three kinds of combining automata, structured in parallel, serial and feedback manners, are investigated based on an algebraic state space approach. Compared with the formal language method, the matrix approach has great advantages in problem description and solution. Because of inconsistent frameworks of these combined automata, we optimize structure matrices by pseudo-commutation of semi-tensor product and power-reducing matrix. In addition, we construct corresponding incidence matrices by labelling to avoid superfluous null elements in the logical matrix occupying storage space. It follows that the observability analysis could be carried out under two polynomial matrices, established from the above algebraic form. Meanwhile, two algorithms, judging whether a combined automaton is initial state observable or current state observable, are presented. Finally, there are two representative examples to actualize our approach.

scholarly journals Controllability, Reachability, and Stabilizability of Finite Automata: A Controllability Matrix Method

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Yalu Li ◽  
Wenhui Dou ◽  
Haitao Li ◽  
Xin Liu
Keyword(s):  
Matrix Method ◽  
Finite Automata ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Form ◽  
Controllability Matrix ◽  
Necessary And Sufficient ◽  
Semitensor Product Of Matrices ◽  
Product Of Matrices ◽  
Inputs And Outputs

This paper investigates the controllability, reachability, and stabilizability of finite automata by using the semitensor product of matrices. Firstly, by expressing the states, inputs, and outputs as vector forms, an algebraic form is obtained for finite automata. Secondly, based on the algebraic form, a controllability matrix is constructed for finite automata. Thirdly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of finite automata by using the controllability matrix. Finally, an illustrative example is given to support the obtained new results.

Stabilization of probabilistic finite automata based on semi-tensor product of matrices

2020 ◽  
Vol 357 (9) ◽  
pp. 5173-5186 ◽  
Author(s):  
Zhipeng Zhang ◽  
Zengqiang Chen ◽  
Xiaoguang Han ◽  
Zhongxin Liu
Keyword(s):  
Tensor Product ◽  
Finite Automata ◽  
Product Of Matrices ◽  
Probabilistic Finite Automata

Language acceptability of finite automata based on theory of semi‐tensor product of matrices

2019 ◽  
Vol 21 (6) ◽  
pp. 2634-2643
Author(s):  
Jumei Yue ◽  
Yongyi Yan ◽  
Zengqiang Chen
Keyword(s):  
Tensor Product ◽  
Finite Automata ◽  
Product Of Matrices

Security and privacy with K-step opacity for finite automata via a novel algebraic approach

2021 ◽  
pp. 014233122110403
Author(s):  
Qian Xu ◽  
Zhipeng Zhang ◽  
Yongyi Yan ◽  
Chengyi Xia
Keyword(s):  
Formal Language ◽  
Polynomial Matrix ◽  
Finite Automata ◽  
Algebraic Approach ◽  
Security And Privacy ◽  
Related Area ◽  
Physical Systems ◽  
The Matrix ◽  
Problem Description ◽  
Necessary And Sufficient

As an important secretive attribute, opacity of cyber-physical systems (CPSs) has attracted considerable attention. Existing works on opacity mainly concentrate on the formal language method by assuming that the intruder tracks partial knowledge of observable transitions. In this paper, under the framework of Boolean semi-tensor product (BSTP) of matrix, we extend the verification of opaque property to algebraic mechanisms that have great advantages in problem description and solution. First, we show that how [Formula: see text]-step opacity problem of nondeterministic finite automata (NFAs) can be transformed to the construction problem of a polynomial matrix that characterizes the state estimation eavesdropped by malicious intruders within the last [Formula: see text] observations. Second, the necessary and sufficient condition of verifying [Formula: see text]-step opacity is obtained, which is equivalent to validate the composition of elements within the polynomial matrix. Finally, the effectiveness of this result is demonstrated by an illustrative example. Taking together, the matrix-based method will be useful to deliver a novel theoretical tool for investigating the privacy-preserving problem in the related area of CPSs.

scholarly journals ηQ Meson Photoproduction in Ultrarelativistic Heavy Ion Collisions

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Gong-Ming Yu ◽  
Gao-Gao Zhao ◽  
Zhen Bai ◽  
Yan-Bing Cai ◽  
Hai-Tao Yang ◽  
...  
Keyword(s):  
Heavy Ion Collisions ◽  
Hadron Collider ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Heavy Quarkonium ◽  
Color Singlet ◽  
Initial State ◽  
Color Octet ◽  
Ion Collisions ◽  
The Matrix

The transverse momentum distributions for inclusive ηc,b meson described by gluon-gluon interactions from photoproduction processes in relativistic heavy ion collisions are calculated. We considered the color-singlet (CS) and color-octet (CO) components within the framework of Nonrelativistic Quantum Chromodynamics (NRQCD) in the production of heavy quarkonium. The phenomenological values of the matrix elements for the color-singlet and color-octet components give the main contribution to the production of heavy quarkonium from the gluon-gluon interaction caused by the emission of additional gluon in the initial state. The numerical results indicate that the contribution of photoproduction processes cannot be negligible for midrapidity in p-p and Pb-Pb collisions at the Large Hadron Collider (LHC) energies.

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