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Conference Papers Year : 2009

Combinable Extensions of Abelian Groups


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 nondisjoint 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.

Dates and versions

inria-00428077 , version 1 (28-10-2009)



Enrica Nicolini, Christophe Ringeissen, Michael Rusinowitch. Combinable Extensions of Abelian Groups. 22nd International Conference on Automated Deduction - CADE-22, Aug 2009, Montreal, Canada. pp.51-66, ⟨10.1007/978-3-642-02959-2_4⟩. ⟨inria-00428077⟩
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