OPTIMIZATION OF MULTIPLE-VALUED LOGIC FUNCTIONS BASED ON PETRI NETS

This paper presents a novel and successful optimization algorithm for optimizing Multiple-valued Logic (MVL) functions based on Petri net th eory. Mathematical properties and Petri net modeling tools to implemen t MVL systems are introduced. On the basis of these properties and mod eling tools, the optimization algorithm can synthesize, analyze and mi nimize an arbitrary quaternary logic function of n-input variables. Th e analysis technique of optimization algorithm is a well-established c oncept from both theories of MVL and Petri nets, and this can be appli ed to specify and optimize any MVL Petri net system. In this paper, Pe tri nets of Galois field have been proposed in order to form a complet e system, which can be used to realize and construct VLSI circuit of a ny MVL function. Based on the Petri nets of Galois field and the propo sed algorithm, the quaternary minimum and maximum functions have been analyzed, minimized, and designed. These applications have demonstrate d the usefulness of optimization algorithm. Based on Petri net theory, the analysis revealed important information about MVL Petri net model ed systems, where this information has been used to evaluate the model ed system and suggest improvements or changes. For evaluation, advanta ges of the proposed method over a conventional logic minimization meth od are presented. Also, we have observed that the MVL Petri nets have the following advantages: Designers can exhibit clearly, simply and sy stematically any complex MVL Petri net model, number of concurrent ope rations is increased, number of places and transitions that are needed to realize a MVL model is very small, and the interconnection problem s can be greatly reduced.