Optimal circuits and transitive automorphism groups

  • Steven Rudich
  • Leonard Berman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)


In this paper we ask, “Can anything be said about a smallest circuit that computes a given function.” We are able to show that for a wide class of functions, which includes all graph problems, an optimal circuit has a restricted structure. For instance, the input wires in an optimal circuit for Hamiltonian Path have at most linear fan-out. This is analogous to the possibly counter-intuitive statement that there is a straight line program for Hamiltonian Path on graphs with n nodes that looks at each edge only O(n2) times.


Boolean Function Hamiltonian Path Graph Function Input String Graph Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Boppana]
    R. B. Boppana, Threshold Functions and Rounded Depth Monotone Circuits, ACM SIGACT 16(1984), 475–479.Google Scholar
  2. [Fagin]
    R. Fagin, M. M. Klawe, N. J. Pippenger, L. Stockmeyer. Bounded depth. polynomial-size circuits for symmetric functions, IBM Research Report RI 4040. Oct. 1983.Google Scholar
  3. [Furst]
    M. Furst, J. B. Saxe, and M. Sipser, Parity, Circuits, and the Polynomial Time Hierarchy, IEEE FOCS 22(1981) 260–270.Google Scholar
  4. [Paul]
    W. J. Paul, Realizing Boolean Functions on Disjoint Sets of Variables. Theoretical Computer Science 2(1976) 383–396.Google Scholar
  5. [Smolensky]
    R. Smolensky, Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity, ACM SIGACT 19(1987).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Steven Rudich
    • 1
  • Leonard Berman
    • 2
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeley
  2. 2.Mathematical Sciences DepartmentT.J. Watson Research CenterYorktown Heights

Personalised recommendations