A Simplifying-Matrix Method to Reduce the Storage Complexity in Studying Finite State Machines in the Framework of STP

Abstract

The storage complexity problem is one of the severe challenges faced by research of finite state machines (FSMs) in the framework of STP, which must be overcome to make theoretical methodologies applicable to real applications. In this brief we propose a simplifying-matrix method to reduce the complexity of storing the dynamic matrix of an FSM when using computers to deal with problems. This method consists of three key components. Firstly, a mapping from logical matrices to logical vectors is proposed to retain effective information and remove large quantities of useless information from dynamic matrices of FSMs. Secondly, an alternative simplified dynamic matrix is constructed. Finally, a mapping from scalars to logical vectors is proposed to optimize the original model of FSMs and preserve the bilinear feature. In addition, we show that the proposed method is also applicable to reduction of the storage complexity of various logic dynamic systems in the framework of STP, such as, game systems, Boolean control networks, fuzzy systems and graphs.