A new method is proposed for rapidly solving expert system applications using Boolean algebra formulations. The method consists of two algorithms, applied after the conventional hierarchical type rules have been converted to Boolean expressions. The first algorithm automatically reduces the expressions to the equivalent of only two levels in a logic network, eliminating all intermediate conclusions, and also minimizes the number of inputs per rule. This algorithm has general application in the condensation of rule systems, and makes possible the use of high speed bit matching in specific solutions. The second algorithm operates on the reduced rule set so that, in a given application, a rapid solution is achieved using the fewest possible items of evidence, or user inputs. It is believed that these algorithms will be particularly useful in applications where high speed solutions are important.