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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 863–877 (Mi semr529)  
Geometry and topology

Homology and bisimulation of asynchronous transition systems and Petri nets

A. A. Husainov

Komsomolsk-on-Amur State Technical University, pr. Lenina, 27, 681013, Komsomolsk-on-Amur, Russia
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Abstract: Homology groups of labelled asynchronous transition systems and Petri nets are introduced. Examples of computing the homology groups are given. It is proved that if labelled asynchronous transition systems are bisimulation equivalent, then they have isomorphic homology groups. A method of constructing a Petri net with given homology groups is presented.
Keywords: bisimulation, homology groups, simplicial complex, trace monoid, partial action, asynchronous system, Petri net.
Received February 1, 2014, published November 27, 2014
Document Type: Article
UDC: 515.14,519.713
MSC: 55U10,68Q85
Language: English
Citation: A. A. Husainov, “Homology and bisimulation of asynchronous transition systems and Petri nets”, Sib. Èlektron. Mat. Izv., 11 (2014), 863–877
Citation in format AMSBIB
\Bibitem{Khu14}
\by A.~A.~Husainov
\paper Homology and bisimulation of asynchronous transition systems and Petri nets
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 863--877
\mathnet{http://mi.mathnet.ru/semr529}
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