Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A practical algorithm for exact array dependence analysis
Communications of the ACM
Analysis of modular arithmetic
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Decision Procedures: An Algorithmic Point of View
Decision Procedures: An Algorithmic Point of View
Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
A Quantifier Elimination Algorithm for Linear Real Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A decision procedure for bit-vectors and arrays
CAV'07 Proceedings of the 19th international conference on Computer aided verification
A quantifier elimination algorithm for linear modular equations and disequations
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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We present an algorithm for existentially quantifying variables from conjunctions of linear modular equalities (LMEs), disequalities (LMDs) and inequalities (LMIs). We use sound but relatively less complete and cheaper heuristics first, and expensive but more complete techniques are used only when required. Our experiments demonstrate that our algorithm outperforms alternative quantifier elimination techniques based on bit-blasting and Omega Test. We also extend this algorithm to work with Boolean combinations of LMEs, LMDs and LMIs.