Search results
Results from the WOW.Com Content Network
Boolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions. Boolean differential calculus concepts are analogous to those of classical differential calculus , notably studying the changes in functions and variables with ...
This means that it should be easy to generalize an algorithm for obtaining coefficients from a truth table by XORing up values of the function from appropriate rows of a truth table, even for hyperdimensional cases (= and above). Between the starting and destination rows of a truth table, some variables have their values remaining fixed: find ...
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
In addition, the derivatives of a bent function are balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change. The maximal nonlinearity means approximating a bent function by an affine (linear) function is hard, a useful property in the defence against linear cryptanalysis.
Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: = + ′ ′, where is any Boolean function, is a variable, ′ is the complement of , and and ′ are with the argument set equal to and to respectively.
The total influence of a Boolean function is also the average sensitivity of the function. The sensitivity of a Boolean function at a given point is the number of coordinates such that if we flip the 'th coordinate, the value of the function changes. The average value of this quantity is exactly the total influence.
The derivative of the function at a point is the slope of the line tangent to the curve at the point. Slope of the constant function is zero, because the tangent line to the constant function is horizontal and its angle is zero. In other words, the value of the constant function, y, will not change as the value of x increases or decreases.
Graphically, this means that an n-ary Boolean function is monotonic when its representation as an n-cube labelled with truth values has no upward edge from true to false. (This labelled Hasse diagram is the dual of the function's labelled Venn diagram, which is the more common representation for n ≤ 3.)