A Complete Neural Network Algorithm for Horn-SAT

Abstract

Neural Networks are mainly used for classification and similar tasks, involving subsymbolic information. Nevertheless, they are also suited to deal with symbolic problems such as logic problem solving and optimization, where it can be made use of the possibility to process several tasks in parallel. Another aspect in parallel problem solving is the existence of a wide range of results given in parallel complexity theory, where parallel algorithms based on parallel random access machines (PRAMs) are designed to reduce time complexity of problem solving. As neural networks consist of units that are much simpler than PRAMs, these results cannot be directly transferred to the design of neural network algorithms. In this paper we therefore show how to combine the fields of symbolic problem solving by means of Neural Networks and parallel complexity theory to develop a neural network algorithm that solves propositional SAT-problems within the time bounds given by the results of complexity theory.