Abstract
We extend first-order logic with successor using the least fixed point operator and the Hamiltonian path generalized quantifier simultaneously, and show that the complexity class captured is PNP: we also obtain a normal form for this logic. We consider the incorporation of the least fixed point operator into other logics capturing NP and see that this may present difficulties in general. We apply our results to obtain, amongst other results, a new complete problem for PNP involving the evaluation of logically defined functions.
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