The complexity of negation-limited networks — A brief survey

  • Michael J. Fischer
Mittwochvormittag Hauptvortrag
Part of the Lecture Notes in Computer Science book series (LNCS, volume 33)


Proving lower bounds on the combinational complexity of concrete functions is a difficult and challenging problem. Previous successes in establishing lower bounds for monotone networks and the known gaps between the monotone and general combinational complexity indicate the key role that negations play in determining combinational complexity.

We have investigated the way in which the complexity of a set of functions F decreases with the use of additional negations beyond the minimum number necessary to realize F. For sets F of maximum inversion complexity, at most a factor of 2 and an additive term of order n2log2n is saved. However, for sets of lower inversion complexity, no interesting bounds are known on the amount of savings possible. Good upper bounds on the amount of such savings would enable lower bounds on combinational complexity to be concluded from lower bounds on the negation-restricted complexity.


Boolean Function Monotone Function Turing Machine Initial Function Combinational Complexity 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Michael J. Fischer
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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