Structured NC

  • Bertha Scholten
  • Jan van Leeuwen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)


We introduce the class Structured NC (or SNC for short), consisting of all problems that can be solved by means of “structured” NC-circuits. A structured circuit is a circuit in which the gates are organized in a number of layers, each with the same number of gates and the same connections between gates in a layer. We will distinguish several subclasses of SNC depending on the depth of the circuits and the fan-in and fan-out of the gates. Relations among these subclasses and between these subclasses and NC and AC will be derived and we will show how to transform circuits from one class into equivalent circuits in other classes. Furthermore for some problems we present structured NC-circuits having fan-in as well as fan-out≤2; for Parallel Prefix Computation and Addition of n-bit numbers these circuits are of depth O(log n) with only O(n) gates in a layer, which is optimal for structured circuits. For Multiplication we will consider three methods and derive structured NC-circuits for them.


Structure Circuit Input Gate Original Circuit Parallel Prefix Dummy Gate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Bertha Scholten
    • 1
  • Jan van Leeuwen
    • 1
  1. 1.Dept. of Computer ScienceUniversity of UtrechtUtrechtthe Netherlands

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