The computational complexity of universality problems for prefixes, suffixes, factors, and subwords of regular languages

Learning Unions of k-Testable Languages

A classical problem in grammatical inference is to identify a language from a set of examples. In this paper, we address the problem of identifying a union of languages from examples that belong to several different unknown languages. Indeed, decomposing a language into smaller pieces that are easier to represent should make learning easier than aiming for a too generalized language. In particular, we consider k-testable languages in the strict sense (k-TSS). These are defined by a set of allowed prefixes, infixes (sub-strings) and suffixes that words in the language may contain. We establish …

Reducing the time complexity of testing for local threshold testability

A locally threshold testable language L is a language with the property that for some non negative integers k and l and for some word u from L, a word v belongs to L if and only if (1) the prefixes [suffixes] of length k-1 of words u and v coincide, (2) the numbers of occurrences of every factor of length k in both words u and v are either the same or greater than l-1. A deterministic finite automaton is called locally threshold testable if the automaton accepts a locally threshold testable language for some l and k. New necessary and sufficient conditions for a deterministic finite automaton …

通过前缀-后缀复制操作生成斐波那契单词

Generating Fibonacci Words via the Prefix--Suffix Duplication Operation

研究通过前缀-后缀复制操作生成斐波那契单词，解决并强化杜米特兰猜想，证明仅用界限为3的前缀复制可从特定斐波那契单词生成其他单词，且界限3最优，还给出线性时间算法。