On state complexity for subword-closed languages

Jérôme Guyot

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arXiv · 2407.10355

On state complexity for subword-closed languages

Jérôme Guyot

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Abstract

This paper investigates the state complexities of subword-closed and superword-closed languages, comparing them to regular languages. We focus on the square root operator and the substitution operator. We establish an exponential lower bound for superword-closed languages for the k-th root. For subword-closed languages we analyze in detail a specific instance of the square root problem for which a quadratic complexity is proven. For the substitution operator, we show an exponential lower bound for the general substitution. We then find some conditions for which we prove a quadratic upper bound.

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BibTeX RIS

Jérôme Guyot. 2024-07-14. On state complexity for subword-closed languages. https://arxiv.org/abs/2407.10355

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