Balanced Boolean function: Difference between revisions

Revision as of 17:03, 7 July 2012

Revision as of 13:37, 12 February 2013

Line 3:

An example of a balanced boolean function is the function that assigns a '''1''' to every [[even number]] and '''0''' to all odd numbers (likewise the other way around). The same applies for functions assigning '''1''' to all positive numbers and '''0''' otherwise.

A Boolean function of n bits is balanced if it takes the value 1 with probability 1⁄2.

A Boolean function of n bits is balanced if it takes the value 1 with probability 1⁄2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random inputs, no input bit is read with probability more than Θ(n-1/2√ log n). We construct a balanced monotone Boolean function and a randomized algorithm computing it for which each bit is read with probability Θ(n-1⁄3 log n). We then show that for any randomized algorithm for evaluating a balanced Boolean function, when the input bits are uniformly random, there is some input bit that is read with probability at least Θ(n-1𔊪). For balanced monotone Boolean functions, there is some input bit that is read with probability at least Θ(n-1𔊫).

== Usage ==