Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Parallel program design: a foundation
Parallel program design: a foundation
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Deductive verification of real-time systems using STeP
Theoretical Computer Science - Special issue on real-time systems and concurrent and distributed software
Distributed Algorithms
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
BDD Based Procedures for a Theory of Equality with Uninterpreted Functions
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
CAVEAT: Technique and Tool for Computer Aided VErification And Transformation
Proceedings of the 7th International Conference on Computer Aided Verification
Proving with BDDs and Control of Information
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
On Shostak's Decision Procedure for Combinations of Theories
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Equational binary decision diagrams
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
NuMDG: a new tool for multiway decision graphs construction
Journal of Computer Science and Technology - Special issue on natural language processing
A BDD-Representation for the logic of equality and uninterpreted functions
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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A Boolean formula is unsatisfiable if and only if its representing binary decision diagram (BDD) is reduced to the single leaf "false". When BDD variables represent first-order atoms including equalities between terms, uninterpreted predicates or linear arithmetic constraints, a path to the "true" leaf in the BDD might not give a model. So BDDs representing unsatisfiable quantifier-free first-order logic formulas may not reduce to the single leaf "false". Decision procedures for combinations of theories can be used to eliminate all those unsatisfiable paths. In a naive approach every path would be considered; this would be very inefficient. We provide efficient algorithms to find general constraints (connections) from unsatisfiable paths to "true" in the BDD. Adding those connections to the BDD will eliminate many paths to "true" at one go. This procedure also ensures that no unnecessary constraint is added. In the context of invariant validation, this gives good results when using BDDs with a rich quantifier-free language.