A moment of perfect clarity I: the parallel census technique

ABSTRACT

We discuss the history and uses of the parallel census technique---an elegant tool in the study of certain computational objects having polynomially bounded census functions. A sequel [GH] will discuss advances (including [CNS95] and Glaßer [Gla00]), some related to the parallel census technique and some due to other approaches, in the complexity-class collapses that follow if NP has sparse hard sets under reductions weaker than (full) truth-table reductions.

INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.1 COMPUTATION BY ABSTRACT DEVICES
      F.1.2 Modes of Computation
          Subjects: Parallelism and concurrency

Additional Classification:
  F. Theory of Computation
  F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES
      F.4.1 Mathematical Logic
          Subjects: Set theory

General Terms:
Theory