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Comparing counting classes for logspace, one-way logspace, and first-order

  • Hans-Jörg Burtschick
Contributed Papers Structural Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)

Abstract

We consider one-way logspace counting classes which are defined via Turing machines that scan their input only in one direction. The one-way logspace counting classes #1L and span-1L are strict subclasses of the corresponding (two-way) logspace classes #L and span-L, resp. We separate the one-way classes 1UL and 1NL which correspond to the classes UL and NL. It follows that F1L ⊂1L ⊂span-lL ⊂#P.

We generalize first-order counting classes to use <, SUCC, and + as linear orderings. It turns out that with respect to certain natural encodings for op ε { <, SUCC, +} the classes #gSo[op] and #gS1[op] are subclasses of #1L and span-1L. It holds that #Π2[<] = #Π1[SUCC] = #Π1[+], and that this class characterizes #P. From that, we obtain a characterization of #P via universally branching alternating logtime Turing machines.

Keywords

Binary Relation Turing Machine Counting Function Computation Path Relation Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Hans-Jörg Burtschick
    • 1
  1. 1.TU - BerlinBerlin

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