正则理想语言中原子的商复杂度
Quotient Complexities of Atoms in Regular Ideal Languages
摘要：
语言$L$与单词$w$的商（左）是语言$w^{-1}L=\{x\mid wx\in L\}$。正则语言$L$的商复杂度是$L$的商复杂度;它等于$L$的状态复杂度，状态复杂度是接受$L$的最小确定性有限自动机的状态数。$L$的一个原子是关系的一个等价类，其中两个词等价，如果对于每个商，它们要么都在商中，要么都不在商中;因此它是$L$的补和非补商的非空交集。一个右理想（分别是左理想和双侧理想）是一个在字母表$Σ$上的语言$L$，它满足$L=LΣ^*$（分别是$L=Σ^*L$和$L=Σ^*LΣ^*$）。我们计算了右、左和双边正则理想的最大原子数和原子的最大商复杂度。
英文摘要：
A (left) quotient of a language $L$ by a word $w$ is the language $w^{-1}L=\{x\mid wx\in L\}$. The quotient complexity of a regular language $L$ is the number of quotients of $L$; it is equal to the state complexity of $L$, which is the number of states in a minimal deterministic finite automaton accepting $L$. An atom of $L$ is an equivalence class of the relation in which two words are equivalent if for each quotient, they either are both in the quotient or both not in it; hence it is a non-empty intersection of complemented and uncomplemented quotients of $L$. A right (respectively, left and two-sided) ideal is a language $L$ over an alphabet $Σ$ that satisfies $L=LΣ^*$ (respectively, $L=Σ^*L$ and $L=Σ^*LΣ^*$). We compute the maximal number of atoms and the maximal quotient complexities of atoms of right, left and two-sided regular ideals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
