TY - GEN
T1 - Amplification and percolation (probabilistic Boolean functions)
AU - Dubiner, Moshe
AU - Zwick, Uri
N1 - Publisher Copyright:
© 1992 IEEE.
PY - 1992
Y1 - 1992
N2 - The authors extend R.B. Boppana's results (1989) in two ways. They first show that his two lower bounds hold for general read-once formulae, not necessarily monotone, that may even include exclusive-or gates. They are then able to join his two lower bounds together and show that any read-once, not necessarily monotone, formula that amplifies (p-1/n,p+1/n) to (2-n,1-2-n) has size of at least Omega (n/sup alpha +2/). This result does not follow from Boppana's arguments and it shows that the amount of amplification achieved by L.G. Valiant (1984) is the maximal achievable using read-once formulae.
AB - The authors extend R.B. Boppana's results (1989) in two ways. They first show that his two lower bounds hold for general read-once formulae, not necessarily monotone, that may even include exclusive-or gates. They are then able to join his two lower bounds together and show that any read-once, not necessarily monotone, formula that amplifies (p-1/n,p+1/n) to (2-n,1-2-n) has size of at least Omega (n/sup alpha +2/). This result does not follow from Boppana's arguments and it shows that the amount of amplification achieved by L.G. Valiant (1984) is the maximal achievable using read-once formulae.
UR - http://www.scopus.com/inward/record.url?scp=84974175050&partnerID=8YFLogxK
U2 - 10.1109/SFCS.1992.267766
DO - 10.1109/SFCS.1992.267766
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AN - SCOPUS:84974175050
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 258
EP - 267
BT - Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
PB - IEEE Computer Society
T2 - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
Y2 - 24 October 1992 through 27 October 1992
ER -