In this paper, some new concepts for hypergraphs are introduced. Based on the previous results, we do further research on cycle structures of hypergraphs and construct a more strictly complete cycle structure system o...In this paper, some new concepts for hypergraphs are introduced. Based on the previous results, we do further research on cycle structures of hypergraphs and construct a more strictly complete cycle structure system of hypergraphs.展开更多
This article deals with the behavior of two-dimensional （2-D） cellular automata （CA） with a special rule under periodic boundary condition by using matrix algebra. The important characteristics of CA have been stu...This article deals with the behavior of two-dimensional （2-D） cellular automata （CA） with a special rule under periodic boundary condition by using matrix algebra. The important characteristics of CA have been studied, such as Garden of Eden （GOE）, maximal transient length, maximal cycle length and so forth. Several necessary and sufficient conditions are provided, which guarantee a given configuration of being a GOE in different cases. Besides, algorithms are proposed to obtain the number of GOEs, the maximal transient length, and the maximal cycle length in such a CA with the rule mentioned above under periodic condition.展开更多
基金Supported by the National Natural Science Foundation of China(No.11626036)Natural Science Foundation of Beijing(No.1174015)
文摘In this paper, some new concepts for hypergraphs are introduced. Based on the previous results, we do further research on cycle structures of hypergraphs and construct a more strictly complete cycle structure system of hypergraphs.
基金supported by the National Natural Science Foundation of China (60473005)the Guangxi Natural Science Foundation (0640061,0832103)
文摘This article deals with the behavior of two-dimensional （2-D） cellular automata （CA） with a special rule under periodic boundary condition by using matrix algebra. The important characteristics of CA have been studied, such as Garden of Eden （GOE）, maximal transient length, maximal cycle length and so forth. Several necessary and sufficient conditions are provided, which guarantee a given configuration of being a GOE in different cases. Besides, algorithms are proposed to obtain the number of GOEs, the maximal transient length, and the maximal cycle length in such a CA with the rule mentioned above under periodic condition.
