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Planar circuits have short specifications

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STACS 85 (STACS 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 182))

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Abstract

A counting argument is used to establish a lower bound of Ω(2n) on the planar circuit size of almost all n-argument Boolean functions. The counting argument exploits the fact that planar circuits can be more concisely specified than general circuits.

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References

  1. N. Blum. A Boolean function requiring 3n network size. Theoret. Comput. Sci. 28 (1984), 337–345.

    Google Scholar 

  2. M.J. Fischer, A.R. Meyer and M.S. Paterson. Ω(n log n) lower bounds on the length of Boolean formulas. SIAM. J. Comput. 11 (1982), 416–427.

    Google Scholar 

  3. M. Furst, J.B. Saxe and M. Sipser. Parity, circuits, and the polynomial-time hierarchy. Math. Syst. Theory 17 (1984), 13–27.

    Google Scholar 

  4. E.A. Lamagna. The complexity of monotone networks for certain bilinear forms, routing problems, sorting, and merging. IEEE Trans. Computers C-28 (1979), 773–782.

    Google Scholar 

  5. R.J. Lipton and R.E. Tarjan. Applications of a planar separator theorem. SIAM J. Comput. 9 (1980), 615–627.

    Google Scholar 

  6. O.B. Lupanov. Ob odnom methode sinteza skhem. Izv. VUZ (Radio fizika) 1 (1958), 120–140.

    Google Scholar 

  7. O.B. Lupanov. Complexity of formula realisation of functions of logical algebra. Problemy Kibernet. 3 (1960), 61–80; Problems of Cybernetics 3 (1962), 782–811.

    Google Scholar 

  8. W.F.McColl and M.S.Paterson. The planar realization of Boolean functions. Theory of Computation Report No. 60, University of Warwick (1984).

    Google Scholar 

  9. E.I. Neciporuk. A Boolean function. Dokl. Akad. Nauk. SSSR 169 (1966), 765–766; Soviet Math. Dokl. 7 (1966), 999–1000.

    Google Scholar 

  10. W.J. Paul. A 2.5n — lower bound on the combinational complexity of Boolean functions. SIAM J. Comput. 6 (1977), 427–443.

    Google Scholar 

  11. J. Riordan and C.E. Shannon. The number of two-terminal series-parallel networks. J. Math. and Phys. 21 (1942), 83–93.

    Google Scholar 

  12. J.E.Savage. The Complexity of Computing. John Wiley and Sons (1976).

    Google Scholar 

  13. J.E.Savage. Planar circuit complexity and the performance of VLSI algorithms. VLSI Systems and Computations, H.T.Kung, B.Sproull and G.Steele (eds.), Computer Science Press (1981), 61–68. Expanded version appears as INRIA Report No. 77, INRIA, Rocquencourt, France (1981).

    Google Scholar 

  14. C.P. Schnorr. Zwei lineare untere schranken für die komplexität Boolescher funktionen. Computing 13 (1974), 155–171.

    Google Scholar 

  15. C.E. Shannon. The synthesis of two-terminal switching circuits. Bell System Tech. J. 28 (1949), 59–98.

    Google Scholar 

  16. W.T. Tutte. A census of planar triangulations. Canadian J. Math. 14 (1962), 21–38.

    Google Scholar 

  17. I. Wegener. Boolean functions whose monotone complexity is of size n 2/log n. Theoret. Comput. Sci. 21 (1982), 213–224.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Warwick, CV4 7AL, Coventry, England

    W. F. McColl

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  1. W. F. McColl
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K. Mehlhorn

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© 1984 Springer-Verlag Berlin Heidelberg

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McColl, W.F. (1984). Planar circuits have short specifications. In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024012

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  • DOI: https://doi.org/10.1007/BFb0024012

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13912-6

  • Online ISBN: 978-3-540-39136-4

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