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Conference publicationsAbstractsXX conferenceThe sequetial growth of a directed acyclic dyadic graphScientific Research Institute for System Analysis of the Russian Academy of Science, Nahimovskiy pr., 36, k. 1, Moscow, 117218, Russia, (495)719-76-51, akrugly@mail.ru 1The Russian Presidential Academy of National Economy and Public Administration, Vernadskogo pr., 82, Moscow, 119571, Russia, tserkovnikov@hotmail.com One of approaches to quantum gravity is a causal set hypothesis. By assumption, spacetime at microscopic level is discrete and forms a causal set. The causal set is a locally finite partially ordered set. Continuous 3+1 dimensional spacetime and matter (in the first place the particles) must be the result of self-organization of the causal set and the consequence of dynamics. We have the following tasks: an investigation of different variants of dynamics, an investigation of generated processes of self-organization, a development of methods for analyses of generated structures. These tasks may be interesting in different areas if the object is a causal set. For example, this is a run of any program. A directed acyclic dyadic graph is considered. All edges are directed. The acyclic graph means that there is not a directed loop. The dyadic graph means that each vertex possesses two incident incoming edges and two incident outgoing edges. A set of vertices is a particular case of a causal set. The dynamics of this graph is a sequential growth. The new vertices are added one by one. Each new vertex is a maximal or minimal element of the causal set of vertices. This is a stochastic dynamics. We have the probability for any variant to add a new vertex. This probability is a function of the structure of existed graph. We assume the causality principle. The probability to add a new maximal vertex can only depend on the subgraph that precedes this vertex. Similarly, the probability to add a new minimal vertex can only depend on the subgraph that follows this vertex. We introduce simple algorithms with additional constraints and results of numerical simulation.
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