State complexity of inversion operations

초록

The reversal operation is well-studied in the literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2(n) (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion (respectively, prefix-inversion) of a language L consists of all strings ux(R) v such that uxv is an element of L (respectively, all strings u(R)x where ux is an element of L). We show that the nondeterministic state complexity of prefix-inversion is Theta(n(2)) and that of inversion is Theta(n(3)). We show that the deterministic state complexity of prefix-inversion is at most 2(n.logn+n) and has lower bound 2(Omega(n log n)) The same lower bound holds for the state complexity of inversion, but for inversion we do not have a matching upper bound. We also study the state complexity of other variants of the inversion operation. (C) 2015 Elsevier B.V. All rights reserved.

키워드