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33rd Annual Symposium on Foundations of Computer Science (FOCS 1992)
Pittsburgh, PA, USA
October 24-October 27
ISBN: 0-8186-2900-2
| ASCII Text | x | ||
| D. Coppersmith, B. Schieber, "Lower bounds on the depth of monotone arithmetic computations," Foundations of Computer Science, IEEE Annual Symposium on, pp. 288-295, 33rd Annual Symposium on Foundations of Computer Science (FOCS 1992), 1992. | |||
| BibTex | x | ||
| @article{ 10.1109/SFCS.1992.267763, author = {D. Coppersmith and B. Schieber}, title = {Lower bounds on the depth of monotone arithmetic computations}, journal ={Foundations of Computer Science, IEEE Annual Symposium on}, volume = {0}, year = {1992}, isbn = {0-8186-2900-2}, pages = {288-295}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1992.267763}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - CONF JO - Foundations of Computer Science, IEEE Annual Symposium on TI - Lower bounds on the depth of monotone arithmetic computations SN - 0-8186-2900-2 SP288 EP295 A1 - D. Coppersmith, A1 - B. Schieber, PY - 1992 KW - tight bound KW - lower bounds KW - computational complexity KW - depth KW - monotone arithmetic computations KW - arithmetic expression KW - binary computation tree KW - alternating 5-3 trees VL - 0 JA - Foundations of Computer Science, IEEE Annual Symposium on ER - | |||
Consider an arithmetic expression of length n involving only the operations (+,*) and non-negative constants. The authors prove lower bounds on the depth of any binary computation tree over the same set of operations and constants that computes such an expression. In their main result they exhibit a family of arithmetic expressions that requires computation trees of depth at least 1.5 log/sub 2/n-O(1). The authors also consider the family of arithmetic expressions defined by alternating 5-3 trees. For this family they show a tight bound of 5/(log/sub 2/15)log/sub 2/n+O(1) on the depth of any computation tree. This is the best known tight bound for any family of arithmetic expressions.
Index Terms:
tight bound, lower bounds, computational complexity, depth, monotone arithmetic computations, arithmetic expression, binary computation tree, alternating 5-3 trees
Citation:
D. Coppersmith, B. Schieber, "Lower bounds on the depth of monotone arithmetic computations," focs, pp.288-295, 33rd Annual Symposium on Foundations of Computer Science (FOCS 1992), 1992
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