In this paper we introduce a new acceptance concept for nondeterministic Turing machines with output device which allows a
characterization of the complexity class
Θ
2
p
= P
NP[log] as a polynomial time bounded class. Thereby the internal structure of the output is essential: it looks at output with maximal
number of mind changes instead of output with maximal value which was realized for the first time by Krentel [Kre88].
Motivated by this characterization we define in a general way two operators, the so called maxCh- and minCh- operator, respectively
which are special types of optimization operators.
Following a paper by Hempel/Wechsung [HW96] we investigate the behaviour of these operators on the polynomial hierarchy. We
prove a collection of relations regarding the interaction of operators maxCh, minCh, $, Θ, Θ, Θ, Sig, C and U. So we get a
tool to show that the maxCh- and minCh- classes are distinct under reasonable structural assumptions. Finally, our proof techniques
allow to solve one of the open questions of Hempel/Wechsung.