Max-Planck-Institut für Informatik
max planck institut
informatik
mpii logo Minerva of the Max Planck Society
 

MPI-I-98-2-007

The most nonelementary theory (a direct lower bound proof)

Vorobyov, Sergei

MPI-I-98-2-007. April 1998, 36 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We give a direct proof by generic reduction that a decidable
rudimentary theory of finite typed sets [Henkin 63, Meyer 74,
Statman 79, Mairson 92] requires space exceeding infinitely
often an exponentially growing stack of twos. This gives
the highest currently known lower bound for a decidable
logical theory and affirmatively answers to Problem 10.13
of [Compton & Henson 90]:

Is there a `natural' decidable theory with a lower bound of the
form $\exp_\infty(f(n))$, where $f$ is not linearly bounded?

The highest previously known lower and upper bounds for `natural'
decidable theories, like WS1S, S2S, are `just' linearly growing
stacks of twos.
Acknowledgement:
References to related material:

To download this research report, please select the type of document that fits best your needs.Attachement Size(s):
MPI-I-98-2-007.ps436 KBytes
Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView
URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1998-2-007
Hide details for BibTeXBibTeX
@TECHREPORT{Vorobyov98-2-007,
  AUTHOR = {Vorobyov, Sergei},
  TITLE = {The most nonelementary theory (a direct lower bound proof)},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-98-2-007},
  MONTH = {April},
  YEAR = {1998},
  ISSN = {0946-011X},
}