Prefix-free languages: Right quotient and reversal

Abstract

We investigate the right quotient and the reversal operations on the class of prefix-free languages. We get the tight bounds n-1 and 2n-2+1 on the state complexity of right quotient and reversal, respectively. To prove the tightness of the bound for reversal, we use a ternary alphabet. Moreover, we prove that this bound cannot be met by any binary language. In the binary case, we get a lower bound 2n-2-7 infinitely often. Our calculations show that this lower bound cannot be exceeded. © 2014 Springer International Publishing.