Private vs. common random bits in communication complexity
Information Processing Letters
On lower bounds for read-k-times branching programs
Computational Complexity
On separating the read-k-times branching program hierarchy
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
A read-once lower bound and a (1, +k)-hierarchy for branching programs
Theoretical Computer Science
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
On the nonapproximability of boolean Function by OBDDs and read-k-times Branching Programs
Information and Computation
Randomization and Nondeterminism Are Comparable for Ordered Read-Once Branching Programs
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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
Tradeoffs between Nondeterminism and Complexity for Communication Protocols and Branching Programs
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
On Multipartition Communication Complexity
STACS '01 Proceedings of the 18th 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
Triangle-Freeness is Hard to Detect
Combinatorics, Probability and Computing
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
On the P versus NP intersected with co-NP question in communication complexity
Information Processing Letters
Bounds on the Fourier coefficients of the weighted sum function
Information Processing Letters
On the P versus NP intersected with co-NP question in communication complexity
Information Processing Letters
On the average sensitivity of the weighted sum function
Information Processing Letters
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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Recent breakthroughs have lead to strong methods for proving lower bounds on the size of branching programs (BPs) with quite weak restrictions. Nevertheless, lower bounds for the randomized and nondeterministic variants of the established BP models still offer many challenges. Here, the knowledge on the randomized case is extended as follows: (i) The so-far open problem of proving that randomization with arbitrary bounded error can be weaker than nondeterminism for read-once BPs is solved in the following strong sense: It is shown that the so-called "weighted sum function" requires strongly exponential size for randomized read-once BPs with error bounded by any constant smaller than 1/2, while both the function and its complement have polynomial size for nondeterministic read-once BPs. (ii) For randomized read-k BPs, an exponential lower bound for a natural, graph-theoretical function that is easy to compute nondeterministically is presented. This is the first such bound for the boolean BP model. The function cl3,n deciding whether an n-vertex graph contains a triangle is obviously easy for nondeterministic read-once BPs while its complement is known to require strongly exponential size in this model. It is proved here that the function still requires size 2驴(k-22-4k驴驴n) for randomized read-k BPs with error at most 2-c22k for some positive constant c.