Disjunctively Linear Logic Nets

Abstract

Three notions are introduced: 1) a class of logic nets with ``disjunctively linear structure,'' 2) ``disjunctively linear behavior'' or logic nets, and 3) ``position diagrams'' to represent logic nets. Through the study of their properties, it is shown that there is a close relationship between disjunctively linear structures and the behavior of logic nets. It is then shown that the state diagrams of Moore and Mealy and the regular expression of Kleene can be considered as particular manifestations of the notion of disjunctive linearity. By means of the notion of disjunctive linearity, a unified treatment is given to state diagrams by Mealy and the logic nets constructed by Copi, Elgot, and Wright from regular expressions. Finally, a discussion is given to the normal form and the position diagram providing a technique for describing disjunctively linear logic nets. Some problems, such as the practical application of disjunctively linear logic nets for hazard-free operation and the minimization of regular expressions through the use of position diagrams, are suggested.