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Sib. Èlektron. Mat. Izv., 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

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.

Full text: PDF file (561 kB)
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UDC: 515.14,519.713
MSC: 55U10,68Q85
Received February 1, 2014, published November 27, 2014
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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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