Three matrix conditions for the reduction of finite automata based on the theory of semi-tensor product of matrices

2019 ◽  
Vol 63 (2) ◽  
Author(s):  
Jumei Yue ◽  
Yongyi Yan ◽  
Zengqiang Chen
Keyword(s):  
Tensor Product ◽  
Finite Automata ◽  
Product Of Matrices

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

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.

Algebraic method of simplifying Boolean networks using semi‐tensor product of Matrices

2019 ◽  
Vol 21 (6) ◽  
pp. 2569-2577 ◽  
Author(s):  
Yongyi Yan ◽  
Jumei Yue ◽  
Zengqiang Chen
Keyword(s):  
Tensor Product ◽  
Algebraic Method ◽  
Boolean Networks ◽  
Product Of Matrices
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