Relative definability of boolean functions via hypergraphs

Relative definability of boolean functions via hypergraphs

The aim of this work is to show how hypergraphs can be used as a systematic tool in the classi!cation of continuous boolean functions according to their degree of parallelism. Intuitively f is “less parallel” than g if it can be de!ned by a sequential program using g as its only free variable. It turns out that the poset induced by this preorder is (as for the degrees of recursion) a sup-semila...

Equational definability and a quasi-ordering on Boolean functions

Earlier work by several authors has focused on defining Boolean function classes by means of functional equations. In [10], it was shown that the classes of Boolean functions definable by functional equations coincide with initial segments of the quasi-ordered set (Ω,≤) made of the set Ω of Boolean functions, suitably quasi-ordered. Furthermore, the classes defined by finitely many equations co...

Exact Transversal Hypergraphs and Application to Boolean μ-Functions

Exact Transversal Hypergraphs and Application to Boolean µ-Functions

Call an hypergraph, that is a family of subsets (edges) from a finite vertex set, an exact transversal hypergraph iff each of its minimal transversals, i.e., minimal vertex subsets that intersect each edge, meets each edge in a singleton. We show that such hypergraphs are recognizable in polynomial time and that their minimal transversals as well as their maximal independent sets can be generat...

Totality, Definability and Boolean Ciruits

1 I n t r o d u c t i o n Adding parallel constants to a p rog ramming language strict ly increase the expressive power of the language, in general. For instance, extending Scot t ' s P C F with parallel-or, one can define any finite continuous funct ion [7]. However, it is an open problem whether parallelism adds expressive power, if we restrict our attent ion to total functions. Total i ty is...