On the Complexity of Model Expansion

  • Antonina Kolokolova
  • Yongmei Liu
  • David Mitchell
  • Eugenia Ternovska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


We study the complexity of model expansion (MX), which is the problem of expanding a given finite structure with additional relations to produce a finite model of a given formula. This is the logical task underlying many practical constraint languages and systems for representing and solving search problems, and our work is motivated by the need to provide theoretical foundations for these. We present results on both data and combined complexity of MX for several fragments and extensions of FO that are relevant for this purpose, in particular the guarded fragment GF k of FO and extensions of FO and GF k with inductive definitions. We present these in the context of the two closely related, but more studied, problems of model checking and finite satisfiability. To obtain results on FO(ID), the extension of FO with inductive definitions, we provide translations between FO(ID) with FO(LFP), which are of independent interest.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Antonina Kolokolova
    • 1
  • Yongmei Liu
    • 2
  • David Mitchell
    • 3
  • Eugenia Ternovska
    • 3
  1. 1.Memorial University of NewfoundlandCanada
  2. 2.Sun Yat-sen UniversityChina
  3. 3.Simon Fraser UniversityCanada

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