CAJ | 학술논문

循环有限自动机是由单个状态生成的有限自动机，任何有限自动机都是有限个循环有限自动机的并。为了进一步探讨循环有限自动机的性质和揭示一般有限自动机和循环有限自动机的关系，本文利用代数的方法，讨论了循环有限自动机的自同态，得出了计算循环有限自动机自同态半群和自同构群的算法；并讨论了一般有限自动机的同态，证明了每一个有限自动机都是有限个循环有限自动机的直和的同态象。
순배유한자동궤시유단개상태생성적유한자동궤，임하유한자동궤도시유한개순배유한자동궤적병。위료진일보탐토순배유한자동궤적성질화게시일반유한자동궤화순배유한자동궤적관계，본문이용대수적방법，토론료순배유한자동궤적자동태，득출료계산순배유한자동궤자동태반군화자동구군적산법；병토론료일반유한자동궤적동태，증명료매일개유한자동궤도시유한개순배유한자동궤적직화적동태상。
A cyclic finite automaton is a finite automaton which is generated by one single state, and each finite automata is the union of some cyclic finite automata. In this paper, in order to further investigate more insightful properties underlying cyclic finite automata and reveal the relationship between general finite automata and cyclic finite automata, by using the algebraic fashion we analyze the endomorphisms of cyclic finite automata, and propose an algorithm for finding the endomorphism semigroup and the automorphism group of a cyclic finite automaton. Moreover, the homomorphisms of general finite automata are discussed, and it is proved that every finite automaton is a homomorphism image of a direct sum of cyclic finite automata.