# 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={P. McKenzie and K. Wagner},
journal={computational complexity},
year={2007},
volume={16},
pages={211-244}
}
• Published 2007
• Mathematics, Computer Science
• 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… Expand

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#### References

SHOWING 1-10 OF 49 REFERENCES
Finite Moniods: From Word to Circuit Evaluation
• Mathematics, Computer Science
• SIAM J. Comput.
• 1997
Parallel Algorithms for Algebraic Problems
• J. Gathen
• Mathematics, Computer Science
• SIAM J. Comput.
• 1984
An Optimal Parallel Algorithm for Formula Evaluation
• Mathematics, Computer Science
• SIAM J. Comput.
• 1992
Isolation, Matching, and Counting Uniform and Nonuniform Upper Bounds
• Computer Science, Mathematics
• J. Comput. Syst. Sci.
• 1999
Integer circuit evaluation is PSPACE-complete
• Ke Yang
• Mathematics, Computer Science
• Proceedings 15th Annual IEEE Conference on Computational Complexity
• 2000
Computing Algebraic Formulas Using a Constant Number of Registers
• Computer Science, Mathematics
• SIAM J. Comput.
• 1992