Unification in the union of disjoint equational theories: combining decision procedures
Journal of Symbolic Computation
Superposition theorem proving for abelian groups represented as integer modules
Theoretical Computer Science - Special issue on rewriting techniques and applications
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Cancellative abelian monoids and related structures in refutational theorem proving (Part I)
Journal of Symbolic Computation
Superposition and Chaining for Totally Ordered Divisible Abelian Groups
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Superposition with completely built-in Abelian groups
Journal of Symbolic Computation
Arithmetic integration of decision procedures
Arithmetic integration of decision procedures
A comprehensive combination framework
ACM Transactions on Computational Logic (TOCL)
${\mathcal{T}}$-Decision by Decomposition
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Automatic Decidability and Combinability Revisited
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Engineering DPLL(T) + Saturation
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Satisfiability Procedures for Combination of Theories Sharing Integer Offsets
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Integrating linear arithmetic into superposition calculus
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Modular termination and combinability for superposition modulo counter arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
A rule-based framework for building superposition-based decision procedures
WRLA'12 Proceedings of the 9th international conference on Rewriting Logic and Its Applications
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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.