On the complexity of planar Boolean circuits

Abstract

We consider planar circuits, formulas and multilective planar circuits. It is shown that planar circuits and formulas are incomparable. An Ω(n logn) lower bound is given for the multilective planar circuit complexity of a decision problem and an Ω(n 3/2) lower bound is given for the multilective planar circuit complexity of a multiple output function.

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Turán, G. On the complexity of planar Boolean circuits. Comput Complexity 5, 24–42 (1995). https://doi.org/10.1007/BF01277954

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Key words

  • Circuit complexity
  • planar graphs

Subject classifications

  • 68Q05
  • 68Q25
  • 68R10