NP$^{\#P}$ = $\exists$PP and other remarks about maximized counting

David Monniaux

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arXiv · 2202.11955

NP$^{\#P}$ = $\exists$PP and other remarks about maximized counting

David Monniaux

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Abstract

We consider the following decision problem DMAX#SAT, and generalizations thereof: given a quantifier-free propositional formula $F(\mathbf{x},\mathbf{y})$, where $\mathbf{x},\mathbf{y}$ are tuples of variables, and a bound $B$, determine if there is $\vec{x}$ such that $\#\{\mathbf{y} \mid F(\mathbf{x},\mathbf{y})\} \geq B$. This is the decision version of the problem of MAX#SAT: finding $\mathbf{x}$ and $B$ for maximal $B$.

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David Monniaux. 2022-02-24. NP$^{\#P}$ = $\exists$PP and other remarks about maximized counting. https://arxiv.org/abs/2202.11955

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