分组语言的运算状态复杂度

A Survey on Operational State Complexity

Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or nondeterministic, finite automaton that recognises it. Operational state complexity is the study of the state complexity of operations over languages. In this survey, we review the state complexities of individual regularity preserving language operations on regular and some subregular languages. Then we revisit the state complexities of the combination of i…

确定性无秩树自动机的操作状态复杂性

Operational State Complexity of Deterministic Unranked Tree Automata

我们考虑的状态复杂性的基本操作的树语言识别的确定性无秩树自动机。对于并和交运算，得到了弱确定树自动机和强确定树自动机的上界和下界。对于树连接，我们建立了一个严格的上限，这是一个不同的顺序比已知的状态复杂度的连接规则字符串语言。我们证明了（n+1）（（m+1）2^n-2^（n-1））-1个垂直状态是足够的，并且在最坏的情况下是必要的，以识别由分别具有m和n个垂直状态的（强或弱）确定性自动机识别的树语言的级联。

正则语言最小泵引理常数的研究

On Minimal Pumping Constants for Regular Languages

本研究针对正则语言，改进并同时调控四种不同泵引理常数，完整分类Savitch泵引理下九种运算的最小泵引理常数范围，解决先前开放问题。

块语言的表示与状态复杂性

On the Representation and State Complexity of Block Languages

提出用长度 k^ℓ 的位图表示等长单词构成的块语言，给出其到最小确定及非确定有限自动机的转换，分析最大状态数与运算状态复杂性，并得到若干更紧上界。

Computational Complexity of $k$-Block Conjugacy

We consider several computational problems related to conjugacy between subshifts of finite type, restricted to $k$-block codes: verifying a proposed $k$-block conjugacy, deciding if two shifts admit a $k$-block conjugacy, and reducing the representation size of a shift via a $k$-block conjugacy. We give a polynomial-time algorithm for verification, and show GI and NP-hardness for deciding conjugacy and reducing representation size, respectively. Our approach focuses on 1-block conjugacies between vertex shifts, from which we generalize to $k$-block conjugacies and to edge shifts. We conclude …