Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Information Processing Letters
The complexity of Boolean functions
The complexity of Boolean functions
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Genetic programming II: automatic discovery of reusable programs
Genetic programming II: automatic discovery of reusable programs
Heuristic minimization of BDDs using don't cares
DAC '94 Proceedings of the 31st annual Design Automation Conference
Efficient data structures for Boolean functions
Discrete Mathematics - Special issue: trends in discrete mathematics
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Using computational learning strategies as a tool for combinatorial optimization
Annals of Mathematics and Artificial Intelligence
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
On the nonapproximability of boolean Function by OBDDs and read-k-times Branching Programs
Information and Computation
On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Learning Ordered Binary Decision Diagrams
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
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OBDDs with a fixed variable ordering are used successfully as data structure in experiments with learning heuristics based on examples. In this paper, it is shown that, for some functions, it is necessary to develop an algorithm to learn also a good OBDD variable ordering. There are functions with the following properties. They have OBDDs of linear size for optimal variable orderings. But for all but a small fraction of all variable orderings one needs large size to represent a list of randomly chosen examples. These properties are shown for simple functions like the multiplexer and the inner product.