Abstract
The root of a language L is the set of all primitive words p such that pn belongs to L for some n ≥ 1. We show that the gap between the time complexity and space complexity, respectively, of a language and that of its root can be arbitrarily great. From this we conclude that there exist regular languages the roots of which are not even context-sensitive. Also we show that the quadratic time complexity for deciding the set of all primitive words by an 1-tape Turing machine is optimal. © Springer-Verlag Berlin Heidelberg 2002.
Cite
CITATION STYLE
Lischke, G. (2002). The root of a language and its complexity*. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2295 LNCS, pp. 272–280). Springer Verlag. https://doi.org/10.1007/3-540-46011-x_23
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