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The monotone circuit problem Q MC is shown to be complete for xed point logic IFP under quantiier free reductions. Enhancing the circuits with an oracle Q leads to a problem complete for IFP(Q). By contrast, if L is any extension of FO with generalized quantiiers, one can always nd a Q such that IFP(Q) is not contained in L(Q). For L = FO(Q MC), we have L(More)
Acknowledgements First of all I would like to thank my supervisor Professor Heinz{Dieter Ebbing-haus. This dissertation would not have been possible without his considerable advice and without all the long discussions we had on almost every detail. Actually I learned a lot beyond this work. Many others have made valuable contributions to this thesis in(More)
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