The compatible-invariant subset of deterministic finite automata（ DFA） is investigated to solve the problem of subset stabilization under the frameworks of semi-tensor product（ STP） of matrices. The concepts of co...The compatible-invariant subset of deterministic finite automata（ DFA） is investigated to solve the problem of subset stabilization under the frameworks of semi-tensor product（ STP） of matrices. The concepts of compatibleinvariant subset and largest compatible-invariant subset are introduced inductively for Moore-type DFA,and a necessary condition for the existence of largest compatible-invariant subset is given. Meanwhile,by using the STP of matrices,a compatible feasible event matrix is defined with respect to the largest compatible-invariant subset.Based on the concept of compatible feasible event matrix,an algorithm to calculate the largest compatible-invariant subset contained in a given subset is proposed. Finally,an illustrative example is given to validate the results.展开更多
基金supported by the National Natural Science Foundation of China(61573199,61573200)
文摘The compatible-invariant subset of deterministic finite automata（ DFA） is investigated to solve the problem of subset stabilization under the frameworks of semi-tensor product（ STP） of matrices. The concepts of compatibleinvariant subset and largest compatible-invariant subset are introduced inductively for Moore-type DFA,and a necessary condition for the existence of largest compatible-invariant subset is given. Meanwhile,by using the STP of matrices,a compatible feasible event matrix is defined with respect to the largest compatible-invariant subset.Based on the concept of compatible feasible event matrix,an algorithm to calculate the largest compatible-invariant subset contained in a given subset is proposed. Finally,an illustrative example is given to validate the results.
