Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Journal of Symbolic Computation
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Term rewriting and all that
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Software—Practice & Experience
An algorithm for reasoning about equality
Communications of the ACM
Algorithms and Data Structures in VLSI Design
Algorithms and Data Structures in VLSI Design
BDD Based Procedures for a Theory of Equality with Uninterpreted Functions
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Automatic verification of Pipelined Microprocessor Control
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
PVS: Combining Specification, Proof Checking, and Model Checking
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Using BDDs with Combinations of Theories
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
µCRL: A Toolset for Analysing Algebraic Specifications
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
State Space Reduction by Proving Confluence
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Model-checking processes with data
Science of Computer Programming
Parameterised boolean equation systems
Theoretical Computer Science - Formal methods for components and objects
Generalizing DPLL and satisfiability for equalities
Information and Computation
Symbolic program analysis using term rewriting and generalization
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
A Term Rewriting Technique for Decision Graphs
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Biconditional BDD: a novel canonical BDD for logic synthesis targeting XOR-rich circuits
Proceedings of the Conference on Design, Automation and Test in Europe
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We allow equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of reduced ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQOBDDs satisfiability and tautology checking can be done in constant time. Several procedures to eliminate equality from BDDs have been reported in the literature. Typical for our approach is that we keep equalities, and as a consequence do not employ the finite domain property. Furthermore, our setting does not strictly require Ackermann's elimination of function symbols. This makes our setting much more amenable to combinations with other techniques in the realm of automatic theorem proving, such as term rewriting. We introduce an algorithm, which for any propositional formula with equations finds an EQ-OBDD that is equivalent to it. The algorithm has been implemented, and applied to benchmarks known from literature. The performance of a prototype implementation is comparable to existing proposals.