On the homology groups of asynchronous transition systems
Dalʹnevostočnyj matematičeskij žurnal, Tome 6 (2005) no. 1, pp. 23-38.

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This work is devoted to the homology groups of the asynchronous transition systems and Petri nets. A parallel product of the asynchronous transition systems is introduced. The Künneth formula for the parallel product is proved.
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A. A. Khusainov; V. V. Tkachenko. On the homology groups of asynchronous transition systems. Dalʹnevostočnyj matematičeskij žurnal, Tome 6 (2005) no. 1, pp. 23-38. http://geodesic.mathdoc.fr/item/DVMG_2005_6_1_a2/

[1] G. Winskel, Events in Computation, ed. Ph. D. Thesis, Dept. of Computer Science, University of Edinburgh, 1980, 289 pp.

[2] M. A. Bednarczyk, Categories of Asynchronous Systems, Report 1/88, ed. Ph. D. Thesis, University of Sussex, 1988, 222 pp. http://www.ipipan.gda.pl/~marek

[3] G. Winskel, M. Nielsen, Categories in Concurrency, Preprint, BRICS-EP-96-WN, Aarhus University, 1996, 58 pp. | MR

[4] A. A. Khusainov, V. V. Tkachenko, “Gruppy gomologii asinkhronnykh sistem perekhodov”, Matematicheskoe modelirovanie i smezhnye voprosy matematiki, cb. nauch. tr., KhGPU, Khabarovsk, 2003, 23–33 http://www.knastu.ru/husainov_site/index.html

[5] A. Husainov, “On the homology of small categories and asynchronous transition systems”, Homology Homotopy Appl., 6:1 (2004), 439–471 {http://www.rmi.acnet.ge/hha} | MR | Zbl

[6] P. Gaucher, “Homotopy invariants of higher dimensional categories and concurrency in computer scienc”, Math. Structures Comput. Sci., 10:4 (2000), 481–524 | DOI | MR | Zbl

[7] P. Gaucher, “About the globular homology of higher dimensional automata”, Cah. Topol. Geom. Differ., 43:2 (2002), 107–156 | MR | Zbl

[8] E. Goubault, The Geometry of Concurrency, Ph. D. Thesis, Ecole Normale Supérieure, 1995, 349 pp. http://www.dmi.ens.fr/~goubault

[9] P. Gabriel, M. Tsisman, Kategorii chastnykh i teoriya gomotopii, Mir, M., 1971, 296 pp. | MR | Zbl

[10] P. J. Hilton, U. Stammbach, A Course in Homological Algebra, Graduate Texts in Mathematics, 4, Springer-Verlag, New York, Heidelberg, Berlin, 1971, 338 pp. | MR

[11] A. Husainov, “Homological dimension theory of small categories”, J. Math. Sci. (New York), 110:1 (2002), 2273–2321 | DOI | MR | Zbl

[12] F. Morace, Finitely presented categories and homology, Tech. report, Univ. Joseph Fourier, 1995, 27 pp. http://www-fourier.ujf-grenoble.fr/PREP/html/a295/a295.html

[13] G. Winskel, M. Nielsen, “Models for Concurrency”, Handbook of Logic in Computer Science, v. IV, ed. Abramsky, Gabbay, Maibaum, Oxford University Press, 1995, 1–148 | MR

[14] M. Nielsen, G. Winskel, “Petri Nets and Bisimulations”, Theoretical Computer Science, 153:1-2 (1996), 211–244 | DOI | MR | Zbl

[15] S. Maklein, Gomologiya, Mir, M., 1966