On a Sufficient Condition for a Matrix to be the Synchronic Distance Matrix of a Marked Graph

Kiyoshi MIKAMI
Hiroshi TAMURA
Masakazu SENGOKU

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A    No.10    pp.1607-1609
Publication Date: 1993/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Nets-Oriented Software Specification and Design)
marked graph,  synchronic distance matrix,  distance matrix,  

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The synchronic distance is a fundamental concept in a Petri net. Marked graphs form a subclass of Petri nets. Given a matrix D, we are interested in the problem of finding a marked graph whose synchronic distance matrix is D. It is wellknown that the synchronic disrance matrix of a marked graph is a distance matrix. In this letter, we give a matrix D such that D is a distance matrix and there does not exist a marked graph whose synchronic distance matrix is D.