Arithmetic Constant-Depth Circuit Complexity Classes

  • Hubie Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


The boolean circuit complexity classes AC 0 ⊆ AC 0[m] ⊆ TC 0 ⊆ NC 1 have been studied intensely. Other than NC 1, they are defined by constant-depth circuits of polynomial size and unbounded fan-in over some set of allowed gates. One reason for interest in these classes is that they contain the boundary marking the limits of current lower bound technology: such technology exists for AC 0 and some of the classes AC 0[m], while the other classes AC 0[m] as well as TC 0 lack such technology.

Continuing a line of research originating from Valiant’s work on the counting class \(\ensuremath{\sharp} P\), the arithmetic circuit complexity classes \(\ensuremath{\sharp} AC^0\) and \(\ensuremath{\sharp} NC^1\) have recently been studied. In this paper, we define and investigate the classes \(\ensuremath{\sharp} AC^0[m]\) and \(\ensuremath{\sharp} TC^0\), new arithmetic circuit complexity classes that are defined by constant-depth circuits and are analogues of the classes AC 0[m] and TC 0.


Boolean Function Closure Property Circuit Complexity Language Class Arithmetic Circuit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hubie Chen
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA

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