The Complexity of Restricted Regular Expressions and the Synthesis Problem for Finite Automata

@article{Leiss1981TheCO,
title={The Complexity of Restricted Regular Expressions and the Synthesis Problem for Finite Automata},
author={Ernst L. Leiss},
journal={J. Comput. Syst. Sci.},
year={1981},
volume={23},
pages={348-354}
}

It is known that for every restricted regular expression of length n there exists a nondeterministic finite automaton with n + 1 states giving rise to the upper bound of 2” + 1 on the number of states of the corresponding reduced automaton. In this note we show that this bound can be attained for all n ) 2, i.e., the upper bound 2” + 1 is optimal. An observation is then made about the synthesis problem for nondeterministic finite automata.