Characterizations of PUNC and precomputation

  • Eric W. Allender
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)


Much complexity-theoretic work on parallelism has focused on the class NC, which is defined in terms of logspace-uniform circuits. Yet P-uniform circuit complexity is in some ways a more natural setting for studying feasible parallelism. In this paper, P-uniform NC (PUNC) is characterized in terms of space-bounded AuxPDA's and alternating Turing Machines with bounded access to the input. We also present a general-purpose parallel computer for PUNC; this characterization leads to an easy proof that NC = PUNC iff all tally languages in P are in NC. The characterizations of PUNC lead to natural methods for modelling precomputation. We show that for many classes of interest, there is a single “universal” table which can be used in place of any table of similar size and complexity, while for certain other classes, no such “universal” table exists.


Turing Machine Circuit Complexity Mathematical System Theory Input Head Precomputed Table 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Eric W. Allender
    • 1
  1. 1.Department of Computer ScienceRutgers UniversityNew BrunswickUSA

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