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Category of asynchronous systems and polygonal morphisms
Ahmet A. Husainov
A weak asynchronous system is a trace monoid with a partial action on a set. A polygonal morphism between weak asynchronous systems commutes with the actions and preserves the inde…
Homology and Bisimulation of Asynchronous Transition Systems and Petri Nets
Ahmet A. Husainov
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 asynch…
Time Estimation Model of Concurrent Computing Systems
Ahmet A. Husainov, E. S. Kudryashova
We consider an asynchronous system with transitions corresponding to the instructions of a computer system. For each instruction, a runtime is given. We propose a mathematical mode…
Homology Groups of Pipeline Petri Nets
Ahmet A. Husainov, E. S. Bushmeleva, T. A. Trishina
We study homology groups of elementary Petri nets for the pipeline systems. We show that the integral homology groups of these nets in dimensions 0 and 1 equal the group of integer…