Explicit construction of linear sized tolerant networks
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q
Journal of Combinatorial Theory Series B
On lower bounds for read-k-times branching programs
Computational Complexity
New lower bounds and hierarchy results for restricted branching programs
Journal of Computer and System Sciences
Neither reading few bits twice nor reading illegally helps much
Discrete Applied Mathematics
Time-space tradeoffs for branching programs
Journal of Computer and System Sciences
Time-space trade-off lower bounds for randomized computation of decision problems
Journal of the ACM (JACM)
A Superpolynomial Lower Bound for (1, +k(n))-Branching Programs
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
New Lower Bounds and Hierarchy Results for Restricted Branching Programs
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
| Hi-index | 5.23 |
The replication number of a branching program is the minimum number R such that along every accepting computation at most R variables are tested more than once; the sets of variables re-tested along different computations may be different. For every branching program, this number lies between 0 (read-once programs) and the total number n of variables (general branching programs). The best results so far were exponential lower bounds on the size of branching programs with R=o(n/logn). We improve this to R@?@en for a constant @e0. This also gives an alternative and simpler proof of an exponential lower bound for (1+@e)n time branching programs for a constant @e0. We prove these lower bounds for quadratic functions of Ramanujan graphs.