Completeness and weak completeness under polynomial-size circuits

  • David W. Juedes
  • Jack H. Lutz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 900)


This paper investigates the distribution and nonuniform complexity of problems that are complete or weakly complete for ESPACE under nonuniform many-one reductions that are computed by polynomial-size circuits (P/Poly-many-one reductions). Every weakly P/Poly-many-one-complete problem is shown to have a dense, exponential, nonuniform complexity core. An exponential lower bound on the space-bounded Kolmogorov complexities of weakly P/Poly-Turing-complete problems is established. More importantly, the P/Poly-many-one-complete problems are shown to be unusually simple elements of ESPACE, in the sense that they obey nontrivial upper bounds on nonuniform complexity (size of nonuniform complexity cores and space-bounded Kolmogorov complexity) that are violated by almost every element of ESPACE. More generally, a Small Span Theorem for P/Poly-many-one reducibility in ESPACE is proven and used to show that every P/Poly-many-one degree -including the complete degree — has measure 0 in ESPACE. (In contrast, almost every element of ESPACE is weakly P-many-one complete.) All upper and lower bounds are shown to be tight.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • David W. Juedes
    • 1
  • Jack H. Lutz
    • 2
  1. 1.Department of Computer ScienceOhio UniversityAthensUSA
  2. 2.Department of Computer ScienceIowa State UniversityAmesUSA

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