Far Eastern Mathematical Journal

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On the homology groups of asynchronous transition systems


A. A. Khusainov, V. V. Tkachenko

2005, issue 1-2, Ñ. 23–38


Abstract
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 Ku?nneth formula for the parallel product is proved.

Keywords:
asynchronous systems, homology of categories

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References

[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.
[4] A. A. Xusainov, V. V. Tkachenko, “Gruppy gomologij asinxronnyx sistem perexodov”, Matematicheskoe modelirovanie i smezhnye voprosy matematiki, cb. nauch. tr., XGPU, Xabarovsk, 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}.
[6] P. Gaucher, “Homotopy invariants of higher dimensional categories and concurrency in computer scienc”, Math. Structures Comput. Sci., 10:4 (2000), 481–524.
[7] P. Gaucher, “About the globular homology of higher dimensional automata”, Cah. Topol. Geom. Differ., 43:2 (2002), 107–156.
[8] E. Goubault, The Geometry of Concurrency, Ph. D. Thesis, Ecole Normale Supe?rieure, 1995, 349 pp., http://www.dmi.ens.fr/~goubault.
[9] P. Gabriel', M. Cisman, Kategorii chastnyx i teoriya gomotopij, Mir, M., 1971, 296 s.
[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.
[11] A. Husainov, “Homological dimension theory of small categories”, J. Math. Sci. (New York), 110:1 (2002), 2273–2321.
[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.
[14] M. Nielsen, G. Winskel, “Petri Nets and Bisimulations”, Theoretical Computer Science, 153:1-2 (1996), 211–244.
[15] S. Maklejn, Gomologiya, Mir, M., 1966.

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