IJPAM: Volume 70, No. 3 (2011)


Zvi Retchkiman Konigsberg
Instituto Politécnico Nacional
CIC - Centro de Investigacion en Computacion
Mineria 17-2, Col. Escandon, Mexico D.F., 11800, MEXICO

Abstract. Serial computer processing systems are characterized by the fact of executing software using a single central processing unit (CPU) while parallel computer processing systems simultaneously use multiple CPU's at the time.

Parallel computer processing systems are an evolution of serial computer processing systems that attempt to emulate what has always been the state of affairs in the natural world: many complex, interrelated events happening at the same time, yet within a sequence. Today, commercial applications provide an equal or greater driving force in the development of faster computers. These applications require the processing of large amounts of data. Some of the arguments which have been used to say why it is better parallel than serial are: save time and/or money, solve larger problems. Besides that there are physical and economical limits to serial computer processing systems. However we would like to be more precise and give a definitive and unquestionable formal proof to justify the claim that parallel computer processing systems are better than serial processing systems. The main objective and contribution of this paper consists in using a formal and mathematical approach to prove that parallel computer processing systems are better than serial computer processing systems (better related to: saving time and/or money and being able to solve larger problems). This is achieved thanks to the theory of Lyapunov stability and max-plus algebra applied to discrete event systems modeled with time Petri nets.

Received: January 15, 2011

AMS Subject Classification: 39A30, 15A80, 34H15

Key Words and Phrases: parallel and serial computer processing systems, Lyapunov methods, max-plus algebra, timed Petri nets

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 3