A right [left] locally testable language S is a language with the property that for some non negative integer k two words u and v in alphabet S are equal in the semi group if (1) the prefix and suffix of the words of length k coincide, (2) the set of segments of length k of the words as well as 3) the order of the first appearance of these segments in prefixes [suffixes] coincide. We present necessary and sufficient condition for graph [semi group] to be transition graph [semi group] of the deterministic finite automaton that accepts right [left] locally testable language and necessary and sufficient condition for transition graph of the deterministic finite automaton with locally idempotent semi group. We introduced polynomial time algorithms for the right [left] local testable problem for transition semi group and transition graph of the deterministic finite automaton based on these conditions. Polynomial time algorithm verifies transition graph of automaton with locally idempotent transition semi group.

中文翻译：

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左 [右] 局部可测试性的多项式时间算法

右 [左] 本地可测试语言 S 是具有以下特性的语言：对于某些非负整数 k，字母 S 中的两个单词 u 和 v 在半群中相等，如果 (1) 长度为 k 的单词的前缀和后缀重合，(2) 单词长度为 k 的段集以及 3) 这些段在前缀 [后缀] 中首次出现的顺序一致。我们给出图[半群]为接受右[左]局部可测试语言的确定性有限自动机的转移图[半群]的充要条件和局部幂等的确定性有限自动机转移图的充要条件半组。我们为基于这些条件的确定性有限自动机的转移半群和转移图的右[左]局部可测试问题引入了多项式时间算法。多项式时间算法用局部幂等转移半群验证自动机的转移图。