Introduction to finite fields and their applications
Introduction to finite fields and their applications
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
On the complexity of branching programs and decision trees for clique functions
Journal of the ACM (JACM)
Separating the eraser Turing machine classes Le, NLe, co-NLe and Pe
Theoretical Computer Science
On the distributional complexity of disjointness
Theoretical Computer Science
Different modes of communication
SIAM Journal on Computing
On lower bounds for read-k-times branching programs
Computational Complexity
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
On separating the read-k-times branching program hierarchy
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The cost of the missing bit: communication complexity with help
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Non-commutative arithmetic circuits: depth reduction and size lower bounds
Theoretical Computer Science
Determinism versus non-determinism for linear time RAMs (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Weak Random Sources, Hitting Sets, and BPP Simulations
SIAM Journal on Computing
Making Nondeterminism Unambiguous
SIAM Journal on Computing
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
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
An Exponential Lower Bound for One-Time-Only Branching Programs
Proceedings of the Mathematical Foundations of Computer Science 1984
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
De-Randomizing BPP: The State of the Art
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
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
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On notions of information transfer in VLSI circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On the Non-Approximability of Boolean Functions by OBDDs and Read-k-Times Branching Programs
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
| Hi-index | 5.23 |
This paper deals with the number of monochromatic combinatorial rectangles required to approximate a boolean function on a constant fraction of all inputs, where each rectangle may use its own partition of the input variables. The main result of the paper is that the number of rectangles required for the approximation of boolean functions in this model is very sensitive to the allowed error. There is an explicitly defined sequence of boolean functions fn on n variables such that fn, has rectangle approximations with a constant number of rectangles and one-sided error 1/3 + o(1) or two-sided error 1/4 + o(1), but, on the other hand, fn requires exponentially many rectangles if the error bounds are decreased by an arbitrarily small constant.As applications of this result, the following separation results for read-once branching programs are obtained. The functions from the main result require only linear size for nondeterministic read-once branching programs and randomized read-once branching programs with two-sided error 1/3 + o(1), while randomized read-once branching programs with constant two-sided error smaller than 1/3 and unambiguous nondeterministic read-once branching programs require exponential size.