Simplified theory of boolean functions

Simplified neural architectures for symmetric boolean functions

The theoretical and practical framework of Field Programmable Neural A rr ays has been de ned to reconcile simple hardware topologies with complex neural architectures: FPNAs lead to powerful neural models whose original data exchange scheme allows to use hardware-friendly neural topologies. This paper addresses preliminary results in the study of the computation pow er of FPNAs. The computatio...

Boolean Functions - Theory, Algorithms, and Applications

A Theory of Boolean Valued Functions and Partitions

In this paper Y denotes a non empty set. Let k, l be elements of Boolean. The functor k ⇒ l is defined by: (Def. 1) k ⇒ l = ¬k ∨ l. The functor k ⇔ l is defined as follows: (Def. 2) k ⇔ l = ¬(k ⊕ l). Let k, l be elements of Boolean. The predicate k ⋐ l is defined by: (Def. 3) k ⇒ l = true. Let us note that the predicate k ⋐ l is reflexive. One can prove the following three propositions: (1) For...

Approximations of pseudo-Boolean functions; applications to game theory

This paper studies the approximation of pseudo-Boolean functions by linear functions and more generally by functions of (at most) a specified degree. Here a pseudo-Boolean function means a real valued function defined on {0, 1} n, and its degree is that of the unique multilinear polynomial that expresses it; linear functions are those of degree at most one. The approximation consists in choosin...

Gate-level Synthesis of Boolean Functions using Information Theory Concepts

In this paper we apply information theory concepts to evolutionary Boolean circuit synthesis. We discuss the schema destruction problem when simple conditional entropy is used as fitness function. The design problem is the synthesis of Boolean functions by using the minimum number of binary multiplexers. We show that the fitness landscape of normalized mutual information exhibits better charact...