Constructive version of Boolean algebra

Constructive version of Boolean algebra

The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we show that his notion of overlap morphism corresponds classically to that of map preserving arbitrary joins. Moreover we prove that the power collection of a set is the free overlap algebra join-generated from the set. Then, we generalize the concept of overlap algebra and o...

Constructive Multilevel Logic Synthesis Under Properties of Boolean Algebra

We describe a new constructive multilevel logic synthesis system that integrates the traditionally separate technology-independent and technology-dependent stages of modern synthesis tools. Dubbed M32, this system is capable of generating circuits incrementally based on both functional as well as structural considerations. This is achieved by maintaining a dynamic structural representation of t...

Some Examples of Constructive and Non-constructive Extensions of the Countable Atomless Boolean Algebra

There are two main results concerning the nature of constructive extensions of the countable atomless Boolean algebra, say 28 a, which appear in [1]. These results are (I) if <& is a constructive extension of 23a, then each element of # is recursive open and regular, and (II) the characterization of the simple constructive extensions 28JJJ) as those for which U is recursive open and regular. We...

Ternary Boolean Algebra

Boolean Algebra Approximations

Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof u...