The Minimum Equivalent DNF Problem and Shortest Implicants

@article{Umans2001TheME,
  title={The Minimum Equivalent DNF Problem and Shortest Implicants},
  author={C. Umans},
  journal={J. Comput. Syst. Sci.},
  year={2001},
  volume={63},
  pages={597-611}
}
  • C. Umans
  • Published 2001
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
We prove that the Minimum Equivalent DNF problem is ?P2-complete, resolving a conjecture due to Stockmeyer. We also consider the complexity and approximability of a related optimization problem in the second level of the polynomial hierarchy, that of finding shortest implicants of a Boolean function. We show that when the input is given as a DNF, this problem is complete for a complexity class above coNP utilizing O(log2n)-limited nondeterminism. When the input is given as a formula or circuit… Expand
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  • 3
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  • 41
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  • 66
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References

SHOWING 1-10 OF 19 REFERENCES
The Minimization Problem for Boolean Formulas
  • 17
On limited nondeterminism and the complexity of the V-C dimension
  • 178
  • PDF
The Boolean isomorphism problem
  • 35
  • PDF
More Complicated Questions About Maxima and Minima, and Some Closures of NP
  • K. Wagner
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1987
  • 182
Polynomial-time algorithms for generation of prime implicants
  • 55
Graph Ramsey theory and the polynomial hierarchy
  • 23
  • PDF
Computational complexity
  • 1,398
  • PDF
The Polynomial-Time Hierarchy
  • L. Stockmeyer
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1976
  • 1,333
Two-level logic minimization: an overview
  • O. Coudert
  • Mathematics, Computer Science
  • Integr.
  • 1994
  • 196
On the Amount of Nondeterminism and the Power of Verifying
  • 58
...
1
2
...