B(2): P(M) DUAL RADIX SYSTEMS - THEORY, DESIGN, AND I(SQUARE)L IMPLEMENTATION.

The upward compatibility of binary Boolean algebra with Post algebra was examined. There exists in a Post algebra, P(m), a single two-element Boolean algebra, B(2) {4}. If the complement operation in P(m) is the pseudo-complement or strong negation, then more than one B(2) to P(m) mapping is possible. For m = 2('N), N an integer greater than one, there are 2('N-1) homomorphic mappings of B(2) into P(m). Standard B(2):P(4) building blocks were designed and constructed with integrated injection logic to demonstrate the practical aspects of the dual radix concept. An algorithm for finding the maximum compatible mapping from B(2) to P(m) for completely and incompletely specified functions was developed. Finally, memory elements, bus design, and basic architecture to support a B(2):P(4) processor were considered and comments concerning a B(2) machine operating in a P(m) host were made

The Relation of Equivalence for Post Algebras and Its Application to Hazard-Free Implementations of Boolean Functions

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics program / DAAB-07-72-C-0259National Science Foundation / NSF GK-15459Ope

An Analysis of Some Relationships Between Post and Boolean Algebras with Application to the Minimization of Higher-Order Boolean Functions

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-67-C-0199National Science Foundation / NSF GK-1545

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Logical reduction of relations: from relational databases to Peirce's reduction thesis

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them, and introduce a new characteristic of relations, ternarity, that measures their `complexity of relating' and allows to refine reduction results. In particular, we refine Peirce's controversial reduction thesis, and show that reducibility behavior is dramatically different on finite and infinite domains