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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

The logic-algebraic equations method in system dynamics


Author: N. V. Nagul
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 4.
Journal: St. Petersburg Math. J. 24 (2013), 645-662
MSC (2010): Primary 03C40; Secondary 08A99, 03C98
Published electronically: May 24, 2013
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Abstract: An algorithm is proposed for constructing conditions that ensure the preservation of properties of many-sorted algebraic systems. The functions and relations of such systems are defined on arbitrary steps in the sense of Bourbaki. Preservation conditions are generated as solutions of logic-algebraic equations. The coupling mappings between systems have a nature of morphisms and their canonical expansions to steps. The method is illustrated by the example of analysis of a dynamical property of a discrete-event system.


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Additional Information

N. V. Nagul
Affiliation: Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Lermontova str. 134, Irkutsk, Russia
Email: sapling@icc.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01258-1
PII: S 1061-0022(2013)01258-1
Keywords: Property preservation, many-sorted algebra, discrete-event system
Received by editor(s): April 1, 2007
Published electronically: May 24, 2013
Additional Notes: Supported by RFBR (grants nos. 12-08-90018-Bel-a and no. 11-07-00655-a) and by the Project no. 10 of the Presidium of SB RAS
Article copyright: © Copyright 2013 American Mathematical Society