Optimization of Multiple-Valued Logic Functions Based on Petri Nets

Ali Massoud HAIDAR  Mititada MORISUE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.10   pp.1607-1616
Publication Date: 1994/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Net Theory and Its Applications)
MVL logic synthesis,  MVL Petri nets,  Galois field algebra,  optimization,  

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This paper presents a novel and successful optimization algorithm for optimizing Multiple-valued Logic (MVL) functions based on Petri net theory. Mathematical properties and Petri net modeling tools to implement MVL systems are introduced. On the basis of these properties and modeling tools, the optimization algorithm can synthesize, analyze and minimize an arbitrary quaternary logic function of n-input variables. The analysis technique of optimization algorithm is a well-established concept from both theories of MVL and Petri nets, and this can be applied to specify and optimize any MVL Petri net system. In this paper, Petri nets of Galois field have been proposed in order to form a complete system, which can be used to realize and construct VLSI circuit of any MVL function. Based on the Petri nets of Galois field and the proposed algorithm, the quaternary minimum and maximum functions have been analyzed, minimized, and designed. These applications have demonstrated the usefulness of optimization algorithm. Based on Petri net theory, the analysis revealed important information about MVL Petri net modeled systems, where this information has been used to evaluate the modeled system and suggest improvements or changes. For evaluation, advantages of the proposed method over a conventional logic minimization method are presented. Also, we have observed that the MVL Petri nets have the following advantages: Designers can exhibit clearly, simply and systematically any complex MVL Petri net nodel, number of concurrent operations is increased, number of places and transitions that are needed to realize a MVL model is very small, and the interconnection problems can be greatly reduced.