UDC 530.12:539.12 A Sequential Growth Dynamics for a Directed Acyclic Dyadic Graph A. L. Krugly Department of Applied Mathematics and Computer Science Scientific Research Institute for System Analysis of the Russian Academy of Science 36, k. 1, Nahimovskiy pr., Moscow, Russia, 117218 A model of discrete spacetime on a microscopic level is considered. <...> It is a directed acyclic dyadic graph (an x-graph). <...> The dyadic graph means that each vertex possesses no more than two incident incoming edges and two incident outgoing edges. <...> This dynamics is a stochastic sequential additions of new vertices one by one. <...> A new vertex can be connected with existed vertex by an edge only if the existed vertex possesses less than four incident edges. <...> The probabilities of different variants of addition of a new vertex depend on the structure of existed x-graph. <...> It is proved that such algorithm of the growth is a consequence of a causality principle and some conditions of symmetry and normalization. <...> The probabilities are represented in a matrix form. <...> The second variant to calculate probabilities is based on these elementary evolution operators. <...> Key words and phrases: causal set, random graph, directed graph. 1. <...> The dyadic graph means that each vertex possesses two incident incoming edges and two incident outgoing edges. <...> By assumption spacetime is discrete on a microscopic level. <...> The author is grateful to A. V. Kaganov and V. V. Kassandrov for extensive discussions on this subject, and I.V. Stepanian for collaboration in a numerical simulation. <...> Krugly A.L. A Sequential Growth Dynamics for a Directed Acyclic Dyadic Graph 125 of x-graph with 3 vertices (Fig. 1b). <...> This loop includes 2 edges in the same direction and 1 edge in opposite direction. where C is a set and ≺ is a binary relation on C satisfying the following properties (x, y, z are general elements of C): This model is the particular case of a causal set. <...> These are the same as for events in Minkowski spacetime. <...> A(x, y) is called an Alexandrov set of the elements x and y or a causal interval or an order interval. <...> The physical meaning of this binary relation ≺ is causal or chronological order. <...> By assumption a causal set describes spacetime and matter on a microscopic level. <...> A causal set approach to quantum gravity has <...>