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Sparsity pp 397-410 | Cite as

Algorithmic Applications

  • Jaroslav Nešetřil
  • Patrice Ossona de Mendez
Chapter
Part of the Algorithms and Combinatorics book series (AC, volume 28)

Abstract

As a particular interpretation, this problem contains the decision problem for first-order logic (that is, the problem of algorithmically deciding whether a first-order formula is universally valid). A negative answer to the Entscheidungsproblem was given by Church and Turing, who proved that it is impossible to decide algorithmically whether statements in arithmetic are true or false.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jaroslav Nešetřil
    • 1
  • Patrice Ossona de Mendez
    • 2
  1. 1.Computer Science Institute of Charles University (IUUK) Department of Applied MathematicsCharles UniversityPragueCzech Republic
  2. 2.Mathématique Sociales (UMR 8557)CNRS Centre d’Analyse et deParisFrance

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