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40th Annual Symposium on Foundations of Computer Science
A NonLinear Time Lower Bound for Boolean Branching Programs
New York, New York
October 17October 18
ISBN: 0769504094
ASCII Text  x  
Miklos Ajtai, "A NonLinear Time Lower Bound for Boolean Branching Programs," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 60, 40th Annual Symposium on Foundations of Computer Science, 1999.  
BibTex  x  
@article{ 10.1109/SFFCS.1999.814578, author = {Miklos Ajtai}, title = {A NonLinear Time Lower Bound for Boolean Branching Programs}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1999}, issn = {02725428}, pages = {60}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFFCS.1999.814578}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  A NonLinear Time Lower Bound for Boolean Branching Programs SN  02725428 SP EP A1  Miklos Ajtai, PY  1999 KW  branching program KW  lower bound KW  Hankel matrix VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We prove that for all positive integer k and for all sufficiently small \math if n is sufficiently large then there is no Boolean (or 2way) branching program of size less than \math which for all inputs \math computes in time kn the parity of the number of elements of the set of all pairs x,y with the property \math. For the proof of this fact we show that if \mathn is a random n by n matrix over the field with 2 elements with the condition that "\math, \math implies \math" then with a high probability the rank of each \math by \math submatrix of A is at least \math, where \math is an absolute constant and n is sufficiently large with respect to \math.
Index Terms:
branching program, lower bound, Hankel matrix
Citation:
Miklos Ajtai, "A NonLinear Time Lower Bound for Boolean Branching Programs," focs, pp.60, 40th Annual Symposium on Foundations of Computer Science, 1999
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