Small Sweeping 2NFAs Are Not Closed Under Complement

A two-way nondeterministic finite automaton is sweeping (snfa) if its input head can change direction only on the end-markers. For every n, we exhibit a language that can be recognized by an n-state snfa but requires \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2^{\varOmega(n)}$\end{document} states on every snfa recognizing its complement.