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}
}
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… CONTINUE READING

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