Meanders and their applications in lower bounds arguments
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Lower bounds for depth-restricted branching programs
Information and Computation
On lower bounds for read-k-times branching programs
Computational Complexity
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
The cost of the missing bit: communication complexity with help
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Determinism versus non-determinism for linear time RAMs (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On randomized one-round communication complexity
Computational Complexity
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Time-space tradeoffs, multiparty communication complexity, and nearest-neighbor problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the size of randomized OBDDs and read-once branching programs for k-stable functions
Computational Complexity
Time-space tradeoffs for branching programs
Journal of Computer and System Sciences
Lower Bounds for Randomized Read-k-Times Branching Programs (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
A Non-Linear Time Lower Bound for Boolean Branching Programs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Super-linear time-space tradeoff lower bounds for randomized computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Randomness versus Nondeterminism for Read-Once and Read- k Branching Programs
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the influence of the variable ordering for algorithmic learning using OBDDs
Information and Computation
Approximating Boolean functions by OBDDs
Discrete Applied Mathematics
On the influence of the variable ordering for algorithmic learning using OBDDs
Information and Computation
On some bounds on the size of branching programs (a survey)
SAGA'05 Proceedings of the Third international conference on StochasticAlgorithms: foundations and applications
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Branching programs are considered as a nonuniform model of computation in complexity theory as well as a data structure for boolean functions in several applications. In many applications (e.g., verification), exact representations are required. For learning boolean functions f on the basis of classified examples, it is sufficient to produce the representation of a function g approximating f. This motivates the investigation of the size of the smallest branching program approximating f. Although several nonapproximability results are contained in the papers on randomized branching programs, these results often do not work for the uniform distribution (which is the most important one in applications). Here, the following nonapproximability results are presented.(1) It is proven that two simple and well-known functions from the branching program literature require exponential size to be approximated with respect to the uniform distribution by OBDDs, which are the most important type of branching programs in applications.(2) The first truly exponential lower bound on the size of approximating syntactic read-k-times branching programs with respect to the uniform distribution and error probability 1/2 - 2-Ω(n), n the input size, is shown. In order to improve upon the best previous results for error probabilities smaller than 1/3, a strong combinatorial lemma from a paper of Ajtai on linear-length branching programs is exploited.