| The Boolean vector function synthesis problem can be stated as follows: Given a truth table with n input variables and m output variables, synthesize a Boolean vector function that describes the table. In this paper we describe a new formulation of the Boolean vector function synthesis problem as a particular type of Satissability Problem. The Satissability Problem is translated into an integ...

A boolean function f(x1, ..., xn) is weakly symmetric if it is invariant under a transitive permutation group on its variables. A boolean function f(x1, ..., xn) is elusive if we have to check all x1,..., xn to determine the output of f(x1, ..., xn) in the worst-case. It is conjectured that every nontrivial monotone weakly symmetric boolean function is elusive, which has been open for a long ti...

In this work we consider a quantum single-error-correcting scheme derived from a oneway entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of the present errorcorrection is to create specific linear Boolean functions which can transform the sixteen error syndromes occurring in the error-correc...

Results from Unification Theory and type inference with coercions are combined to produce a new method for performing strictness analysis of functional programs. A formal deduction system is developed in which extended types are derivable for terms of the A-calculus. These extended types contain Boolean rings describing the reduction behaviour of terms. Algorithms implementing the method are de...

A nearest neighbor representation of a Boolean function is set positive and negative prototypes in Rn such that the has value 1 on an input iff closest prototype positive. For k-nearest majority classification k considered. The complexity minimal number needed to represent function. We give several bounds for this measure. Separations are given between cases when can be real or required Boolean...

This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a renormalization group transformation that maps an arbitrary Boolean function of N Boolean variables to one of N −1 variables. When this transformation is applie...

Suppose that Y n is obtained by observing a uniform Bernoulli random vector X through a binary symmetric channel with crossover probability α. The “most informative Boolean function” conjecture postulates that the maximal mutual information between Y n and any Boolean function b(X) is attained by a dictator function. In this paper, we consider the “complementary” case in which the Boolean funct...

A Boolean function is a function that produces a Boolean value output by logical calculation of Boolean inputs. It plays key roles in programing algorithms and design of circuits. Minimization of Boolean function is able to optimize the algorithms and circuits. Quine-McCluskey (QM) method is one of the most powerful techniques to simplify Boolean expressions. Compared to other techniques, QM me...