The operators minCh and maxCh on the polynomial hierarchy
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 = PNP[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.
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