A practical algorithm for exact array dependence analysis
Communications of the ACM
On the Automata Size for Presburger Arithmetic
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Enhancing modular OO verification with separation logic
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
A Quantifier Elimination Algorithm for Linear Real Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
(LIA) - Model Evolution with Linear Integer Arithmetic Constraints
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Generalizing DPLL to Richer Logics
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Effective Quantifier Elimination for Presburger Arithmetic with Infinity
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
LIRA: handling constraints of linear arithmetics over the integers and the reals
CAV'07 Proceedings of the 19th international conference on Computer aided verification
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
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
Virtual substitution for SMT-solving
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
A small model theorem for rectangular hybrid automata networks
FMOODS'12/FORTE'12 Proceedings of the 14th joint IFIP WG 6.1 international conference and Proceedings of the 32nd IFIP WG 6.1 international conference on Formal Techniques for Distributed Systems
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This paper develops abstract quantifier elimination procedures for linear arithmetic over the reals and integers. They are formulated as theory solvers in the context of an abstract DPLL-based search. The resulting procedures allow the solvers to maintain integral control of the search process. We also evaluate this procedure and compare it with several alternatives. So far, the evaluation indicates that the proposed approach has some compelling advantages.