2024/07/14 by Guyot, Jérôme
#FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.2407.10355
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.