Two boolean functions f, g : {0, 1} → {0, 1} are isomorphic if they are identical up to relabeling of the input variables. We consider the problem of testing whether two functions are isomorphic or far from being isomorphic with as few queries as possible. In the setting where one of the functions is known in advance, we show that the non-adaptive query complexity of the isomorphism testing pro...

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

This paper is concerned with the problem of Boolean approximation in the following sense: given a Boolean function class and an arbitrary Boolean function, what is the function’s best proxy in the class? Specifically, what is its strongest logical consequence (or envelope) in the class of affine Boolean functions. We prove various properties of affine Boolean functions and their representation ...

In Boolean algebra, true statements are denoted 1 and false statements are denoted 0. A Boolean function acts on a set of these Boolean values and outputs a set of Boolean values (usually just one). The most common Boolean operators used are NOT, AND, OR, and XOR. 2.1 NOT NOT is a Boolean function that takes in one Boolean value and outputs its negation. Let x be a Boolean variable. NOT(x) is d...

The aim of this paper is to completely classify all aggregation functions based on the notion of arity gap. We first establish explicit descriptions of the arity gap of the Lovász extensions of pseudo-Boolean functions and, in particular, of the Choquet integrals. Then we consider the wider class of order-preserving functions between arbitrary, possibly different, posets, and show that similar ...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ⌈log 2 (n+ 1)⌉ NOT gates are sufficient to compute any Boolean function on n variables. In this paper, we consider circuits computing non-deterministically and dete...