Year: 2026
Type: preprint
Abstract: We investigate the nondeterministic state complexity of the square-root operation $\sqrt{L}=\{\,w \mid ww\in L\,\}$ on regular languages represented by nondeterministic finite automata. For an $n$-state NFA accepting $L$, it was previously known that $\sqrt{L}$ can be accepted by an NFA with at most $n^{3}$ states, while the best lower bound was only (n-1)(n-2)(n-3). In this paper, we close this gap completely and prove that $n^{3}$ states are sufficient and necessary in the worst case.
Source: arXiv (Cornell University)
Author: Onishchenko, Sergey
Institution: St Petersburg University
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G3470516004, G6444257319
OpenAlex ID: W7160407607
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