${\mathrm{Pal}}^k$ Is Linear Recognizable Online

Abstract

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 $L\cdot \mathrm{Pal}$, where $\mathrm{Pal}$ is the language of all nonempty palindromes. Hence for every fixed positive $k$, ${\mathrm{Pal}}^k$ is online recognizable in linear time and space. Thus we solve an open problem posed by Galil and Seiferas in 1978.

18 pages, 5 figures, presented in SOFSEM 2015