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引用次数: 2
摘要
的新分类任意细胞自动机(CA) Z d研究考虑的所有排列的设置(集团)附近ν和州组问:两个CA (Z d, Q, f,νA)和(B Z d, Q, f,νB)被称为automorphisc,如果有一对排列ν(π,p)和Q,分别,(f B,νB) = (p−1 fπp,νπ),在νπ表示ν的排列和fπ代表一个排列的参数的本地函数f对应νπ。这种自同构自然地引起CA的分类,这样它通常保留CA的全局属性直到置换。作为该理论的一个典型例子,256个一维3近邻2态CA的局部函数被划分为46类。并给出了类的满射性、注入性和可逆性的计算机测试。
A new classification of arbitrary cellular automata (CA for short) in Z d is studied considering the set (group) of all permutations of the neighborhood ν and state set Q. Two CA (Z d, Q, f A, ν A) and (Z d, Q, f B, ν B) are called automorphisc, if there is a pair of permutations (π, p) of ν and Q, respectively, such that (f B, ν B) = (p −1 f A πp, ν A π), where ν π denotes a permutation of ν and f π denotes a permutation of arguments of local function f corresponding to ν π. This automorphissm naturally induces a classification of CA, such that it generally preserves the global properties of CA up to permutation. As a typical example of the theory, the local functions of 256 ECA (1-dimensional 3-nearest neighbors 2-states CA) are classified into 46 classes. We also give a computer test of surjectivity, injecitivity and reversibility of the classes.
期刊介绍:
Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
solutions by mathematical methods of problems emerging in computer science
solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to):
theory of computing,
complexity theory,
algorithms and data structures,
computational aspects of combinatorics and graph theory,
programming language theory,
theoretical aspects of programming languages,
computer-aided verification,
computer science logic,
database theory,
logic programming,
automated deduction,
formal languages and automata theory,
concurrency and distributed computing,
cryptography and security,
theoretical issues in artificial intelligence,
machine learning,
pattern recognition,
algorithmic game theory,
bioinformatics and computational biology,
quantum computing,
probabilistic methods,
algebraic and categorical methods.