A new type of computer for problems in propositional logic, with greatly reduced scanning procedures

Abstract

A simple scanning-type binary logical computer starts by assigning the truth-value 0 to all the variables (propositions) and systematically executes a binary count until the truth value 1 is assigned to all variables. With n variables a scan of 2 n steps is then needed. At each step, all the logical constraints usually are tested simultaneously and only when all are satisfied is a solution to the problem obtained. The principle, and the machine, described here give a greatly compressed procedure; they are such that the constraints are examined individually, not simultaneously; if one or more is unsatisfied, a simple criterion is acted upon which greatly reduces the total number of steps required to find the first solution or any number of solutions. A further criterion is established when the last solution has been found, and the machine may be stopped. It is thought that this short-cut procedure may be of value to scanning-type logical computers for working with large numbers of variables.