Combinable Extensions of Abelian Groups

  • Enrica Nicolini
  • Christophe Ringeissen
  • Michaël Rusinowitch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)


The design of decision procedures for combinations of theories sharing some arithmetic fragment is a challenging problem in verification. One possible solution is to apply a combination method à la Nelson-Oppen, like the one developed by Ghilardi for unions of non-disjoint theories. We show how to apply this non-disjoint combination method with the theory of abelian groups as shared theory. We consider the completeness and the effectiveness of this non-disjoint combination method. For the completeness, we show that the theory of abelian groups can be embedded into a theory admitting quantifier elimination. For achieving effectiveness, we rely on a superposition calculus modulo abelian groups that is shown complete for theories of practical interest in verification.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Enrica Nicolini
    • 1
  • Christophe Ringeissen
    • 1
  • Michaël Rusinowitch
    • 1
  1. 1.LORIA & INRIA Nancy Grand EstFrance

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