Skip to main content
Log in

Complexity hierarchies for Boolean functions

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

Circuit size and depth are two important complexity measures for a Boolean function. Uniform hierarchies are shown to exist with respect to each of these measures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Borodin, A.: On relating time and space to size and depth. SIAM J. Comput. 6, 733–744 (1977)

    Google Scholar 

  2. Gilbert, E.N.: Lattice theoretic properties of frontal switching functions. J. Math. and Phys. 33, 57–97 (1954)

    Google Scholar 

  3. Kodes, L., Specker, E.: Lengths of formulas and elimination of quantifiers I. In: Contributions to mathematical logic (K. Schutte, ed.), pp. 175–188. Amsterdam: North-Holland 1968

    Google Scholar 

  4. Khrapchenko, V.M.: Complexity of realisation of symmetric algebraic logic functions on finite bases. Problemy Kibernet. 31, 231–234 (1976)

    Google Scholar 

  5. Lupanov, O.B.: Ob odnom metode sinteza skhem. Izv. VUZ (Radiofizika) 1, 120–140 (1958)

    Google Scholar 

  6. McColl, W.F.: The circuit depth of symmetric Boolean functions. J. Comput. System Sci. 17, 108–115 (1978)

    Google Scholar 

  7. Paterson, M.S.: An introduction to Boolean function complexity. Astérisque 38–39, 183–201 (1976); also appeared as Stanford Computer Science Report STAN-CS-76-557, Stanford University, 1976

    Google Scholar 

  8. Paul, W.J.: Realizing Boolean functions on disjoint sets of variables. Theoret. Comput. Sci. 2, 383–396 (1976)

    Google Scholar 

  9. Pippenger, N, Fischer, M.J.: Relations among complexity measures. IBM Research Report RC 6569, Yorktown Heights, 1977

  10. Reznik, V.I.: The realization of monotonic functions by means of networks consisting of functional elements. Soviet Physics Dokl. 6, 558–561 (1962)

    Google Scholar 

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

    Google Scholar 

  12. Schnorr, C.P.: Zwei lineare untere Schranken für die Komplexität Boolescher Funktionen. Computing 13, 155–171 (1974)

    Google Scholar 

  13. Schnorr, C.P.: The combinational complexity of equivalence. Theoret. Comput. Sci. 1, 289–295 (1976)

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

McColl, W.F. Complexity hierarchies for Boolean functions. Acta Informatica 11, 71–77 (1978). https://doi.org/10.1007/BF00264601

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00264601

Keywords

Navigation