Homology Groups of a Pipeline Petri Net
https://doi.org/10.18255/1818-1015-2013-2-92-103
Abstract
Petri net is said to be elementary if every place can contain no more than one token. In this paper, it is studied topological properties of the elementary Petri net for a pipeline consisting of n functional devices. If the work of the functional devices is considered continuous, we can come to some topological space of “intermediate” states. In the paper, it is calculated the homology groups of this topological space. By induction on n, using the Addition Sequence for homology groups of semicubical sets, it is proved that in dimension 0 and 1 the integer homology groups of these nets are equal to the group of integers, and in the remaining dimensions are zero. Directed homology groups are studied. A connection of these groups with deadlocks and newsletters is found. This helps to prove that all directed homology groups of the pipeline elementary Petri nets are zeroth.
About the Authors
A. A. Husainov
Komsomolsk-on-Amur State Technical University
Russian Federation
Russian Federation
профессор, доктор физико-математических наук,
Lenina prosp., 27, Komsomolsk-on-Amur, 681013, Russia
E. S. Bushmeleva
Komsomolsk-on-Amur State Technical University
Russian Federation
Russian Federation
аспирант,
Lenina prosp., 27, Komsomolsk-on-Amur, 681013, Russia
T. A. Trishina
Komsomolsk-on-Amur State Technical University
Russian Federation
Russian Federation
студентка,
Lenina prosp., 27, Komsomolsk-on-Amur, 681013, Russia
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Review
For citations:
Husainov A.A., Bushmeleva E.S., Trishina T.A. Homology Groups of a Pipeline Petri Net. Modeling and Analysis of Information Systems. 2013;20(2):92-103. (In Russ.) https://doi.org/10.18255/1818-1015-2013-2-92-103
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