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Verification Tools for Checking some kinds of Testability
arXiv - CS - Formal Languages and Automata Theory Pub Date : 2021-06-04 , DOI: arxiv-2106.02312
A. N. Trahtman

A locally testable language L is a language with the property that for some non negative integer k, called the order of local testability, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k + 1 and (2) the set of intermediate substrings of length k of the word u. For given k the language is called k-testable. The local testability has a wide spectrum of generalizations. A set of procedures for deciding whether or not a language given by its minimal automaton or by its syntactic semigroup is locally testable, right or left locally testable, threshold locally testable, strictly locally testable, or piecewise testable was implemented in the package TESTAS written in C=C++. The bounds on order of local testability of transition graph and order of local testability of transition semigroup are also found. For given k, the k-testability of transition graph is verified. We consider some approaches to verify these procedures and use for this aim some auxiliary programs. The approaches are based on distinct forms of presentation of a given finite automaton and on algebraic properties of the presentation. New proof and fresh wording of necessary and sufficient conditions for local testability of deterministic finite automaton is presented.

中文翻译:

用于检查某些可测试性的验证工具

本地可测试语言 L 是一种语言,它具有以下特性:对于某个非负整数 k,称为本地可测试性顺序,单词 u 是否在语言 L 中取决于(1)单词 u 的前缀和后缀长度为 k + 1 和 (2) 单词 u 的长度为 k 的中间子串的集合。对于给定的 k,该语言称为 k-testable。局部可测试性具有广泛的概括性。一组用于确定由其最小自动机或句法半群给出的语言是否可局部测试、左右局部可测试、阈值局部可测试、严格局部可测试或分段可测试的程序在编写的 TESTAS 包中实现C=C++。还找到了转移图局部可测性阶和转移半群局部可测性阶的界限。对于给定的k,验证了转移图的k-testability。我们考虑了一些方法来验证这些程序并为此使用一些辅助程序。这些方法基于给定有限自动机的不同表示形式和表示的代数特性。提出了确定性有限自动机局部可测试性的充分必要条件的新证明和新措辞。这些方法基于给定有限自动机的不同表示形式和表示的代数特性。提出了确定性有限自动机局部可测试性的充分必要条件的新证明和新措辞。这些方法基于给定有限自动机的不同表示形式和表示的代数特性。提出了确定性有限自动机局部可测试性的充分必要条件的新证明和新措辞。
更新日期:2021-06-07
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