Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Implicit and incremental computation of primes and essential primes of Boolean functions
DAC '92 Proceedings of the 29th ACM/IEEE Design Automation Conference
Polynomial-time algorithms for generation of prime implicants
Journal of Complexity
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Approximation and decomposition of binary decision diagrams
DAC '98 Proceedings of the 35th annual Design Automation Conference
Abstract interpretation using typed decision graphs
Science of Computer Programming
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
On the Complexity and Inapproximability of Shortest Implicant Problems
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Formal analysis of synchronous circuits
Formal analysis of synchronous circuits
Cloning-based context-sensitive pointer alias analysis using binary decision diagrams
Proceedings of the ACM SIGPLAN 2004 conference on Programming language design and implementation
Boolean Functions
Techniques for scaling up analyses based on pre-interpretations
ICLP'05 Proceedings of the 21st international conference on Logic Programming
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Inferring Congruence Equations Using SAT
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Bit-precise reasoning with affine functions
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
Approximate quantifier elimination for propositional boolean formulae
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Existential quantification as incremental SAT
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
SAS'12 Proceedings of the 19th international conference on Static Analysis
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Despite the ubiquity of ROBDDs in program analysis, and extensive literature on ROBDD minimisation, there is a dearth of work on approximating ROBDDs. The need for approximation arises because many ROBDD operations result in an ROBDD whose size is quadratic in the size of the inputs. Furthermore, if ROBDDs are used in abstract interpretation, the running time of the analysis is related not only to the complexity of the individual ROBDD operations but also the number of operations applied. The number of operations is, in turn, constrained by the number of times a Boolean function can be weakened before stability is achieved. This paper proposes a widening that can be used to both constrain the size of an ROBDD and also ensure that the number of times that it is weakened is bounded by some given constant. The widening can be used to either systematically approximate from above (i.e. derive a weaker function) or below (i.e. infer a stronger function).