Abstract. We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using this structure, we present simple and efficient solutions for a number of problems involving palindromes.
Threshold languages, which are the (k/(k−1)) + -free languages over k-letter alphabets with k ≥ 5, are the minimal infinite power-free languages according to Dejean's conjecture, which is now proved for all alphabets. We study the growth properties of these languages. On the base of obtained structural properties and computerassisted studies we conjecture that the growth rate of complexity of the threshold language over k letters tends to a constantα ≈ 1.242 as k tends to infinity.Mathematics Subject Classification. 68Q70, 68R15.
Given a language L that is online recognizable in linear time and space, we construct a linear time and space online recognition algorithm for the language L · Pal, where Pal is the language of all nonempty palindromes. Hence for every fixed positive k, Pal k is online recognizable in linear time and space. Thus we solve an open problem posed by Galil and Seiferas in 1978.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.