# The Complexity of Membership Problems for Circuits Over Sets of Natural Numbers

@article{McKenzie2007TheCO,
title={The Complexity of Membership Problems for Circuits Over Sets of Natural Numbers},
author={Pierre McKenzie and Klaus W. Wagner},
journal={computational complexity},
year={2007},
volume={16},
pages={211-244}
}
• Published 27 February 2003
• Mathematics
• computational complexity
Abstract.The problem of testing membership in the subset of the natural numbers produced at the output gate of a {$$\bigcup, \bigcap, ^-, +, \times$$} combinational circuit is shown to capture a wide range of complexity classes. Although the general problem remains open, the case {$$\bigcup, \bigcap, +, \times$$} is shown NEXPTIME-complete, the cases {$$\bigcup, \bigcap, ^-, \times$$ }, {$$\bigcup, \bigcap, \times$$}, {$$\bigcup, \bigcap, +$$} are shown PSPACE-complete, the case {\bigcup…
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