THE RANGES OF STATE COMPLEXITIES FOR COMPLEMENT, STAR, AND REVERSAL OF REGULAR LANGUAGES
Galina Jirásková · International Journal of Foundations of Computer Science · 2014
We examine the deterministic and nondeterministic state complexity of complements, stars, and reversals of regular languages. Our results are as follows: (1) The nondeterministic state complexity of the complement of an n-state nfa language over a five-letter alphabet may reach each value from log n to 2n. (2) The state complexity of the star (reversal) of an n-state dfa language over a growing alphabet may reach each value from 1 to [Formula: see text] (from log n to 2n, respectively). (3) The nondeterministic state complexity of the star (reversal) of an n-state nfa binary language may reach each value from 1 to n + 1 (from n - 1 to n + 1, respectively). We also obtain some partial results on the nondeterministic state complexity of complements of binary regular languages. As a bonus, we get an exponential number of values that are non-magic in the binary case.