5 research outputs found
Tensor transform of Boolean functions and related algebraic and probabilistic properties
We introduce a tensor transform for Boolean functions that covers the algebraic normal and Walsh transforms but which also allows for the definition of new, probabilistic and weight transforms, relating a function to its bias polynomial and to the weights of its subfunctions respectively. Our approach leads to easy proofs for some known results and to new properties of the aforecited transforms. Finally, we present a new probabilistic characteristic of a Boolean function that is defined by its algebraic normal and probabilistic transforms over the reals
Tensor transform of Boolean functions and related algebraic and probabilistic properties
We introduce a tensor transform for Boolean functions that covers the algebraic normal and Walsh transforms but which also allows for the definition of new, probabilistic and weight transforms, relating a function to its bias polynomial and to the weights of its subfunctions respectively. Our approach leads to easy proofs for some known results and to new properties of the aforecited transforms. Finally, we present a new probabilistic characteristic of a Boolean function that is defined by its algebraic normal and probabilistic transforms over the reals
Tensor transform of Boolean functions and related algebraic and probabilistic properties
We introduce a tensor transform for Boolean functions that covers
the algebraic normal and Walsh transforms but which also allows
for the definition of new, probabilistic and weight transforms,
relating a function to its bias polynomial and to the weights of
its subfunctions respectively. Our approach leads to easy proofs
for some known results and to new properties of the aforecited
transforms. Several new results about algebraic and correlation
properties that depend on the weight transform of Boolean
functions are proved. Finally, we present a new probabilistic
characteristic of a Boolean function that is defined by its
algebraic normal and probabilistic transforms over the reals
Tensor Transform of Boolean Functions and Related Algebraic and Probabilistic Properties
Abstract. We introduce a tensor transform for Boolean functions that covers the algebraic normal and Walsh transforms but which also allows for the definition of new, probabilistic and weight transforms, relating a function to its bias polynomial and to the weights of its subfunctions respectively. Our approach leads to easy proofs for some known results and to new properties of the aforecited transforms. Several new results about algebraic and correlation properties that depend on the weight transform of Boolean functions are proved. Finally, we present a new probabilistic characteristic of a Boolean function that is defined by its algebraic normal and probabilistic transforms over the reals