On Block Sensitivity and Fractional Block Sensitivity

We investigate the relation between the block sensitivity bs( f ) and fractional block sensitivity fbs( f ) complexity measures of Boolean functions. While it is known that fbs( f ) = O(bs( f ) 2 ), the best known separation achieves fbs( f ) = ( ( 3√(2))^ - 1 + o( 1 ))bs( f )^3/2 . We improve the constant factor and show a family of functions that give fbs( f ) = (6 −1/2 − o (1)) bs( f ) 3/2 .