$\mathrm{Pal}^k$ Is Linear Recognizable Online
Dmitry Kosolobov, Mikhail Rubinchik, Arseny M. Shur
TL;DR
This paper presents a linear time and space online recognition algorithm for languages formed by concatenating a given online recognizable language with palindromes, solving a decades-old open problem.
Contribution
It introduces a method to recognize the language $ ext{Pal}^k$ online in linear time and space, extending previous recognition capabilities.
Findings
Linear recognition algorithm for $ ext{Pal}^k$
Solves open problem from 1978
Applicable to fixed positive $k$
Abstract
Given a language that is online recognizable in linear time and space, we construct a linear time and space online recognition algorithm for the language , where is the language of all nonempty palindromes. Hence for every fixed positive , is online recognizable in linear time and space. Thus we solve an open problem posed by Galil and Seiferas in 1978.
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Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · Cryptography and Data Security