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### THE DISCRETE MODEL OF SPACETIME AND THE BINARY PREGEOMETRY OF VLADIMIROV

#### Krugly A.L.

The discrete model of spacetime is considered. This is a finite connected directed acyclic graph. The indegree and the outdegree of each vertex is no more than 2. Then this graph is called x-graph. Vertices are elementary events. Edges are elementary causal relations. Vertices and edges are nondivisible. They have no intrinsic properties. All properties are the topology of x-graph. The world line of elementary particle is considered as a sequence of repetetive structures. There are two tasks. The first is a dynamics of x-graph. This task is not considered. The second task is the identification of topological structures and phisical objects, topological properties and phisical quantities. To solve this task we need a correspondence the topology of x-graph and quantum discription. In quantum discription we use complex numbers. In topology of x-graph we use natural numbers as the number of vertices, the number of edges, the number of some pathes and so on. We get complex numbers for topology of xgraph by Fourier analysis. Some properties of x-graph are proved. Using these properties the topology of x-graph can be described by binary systems of complex relations of Vladimirov. We can use the results of Vladimirov for analysis and physical interpretation of x-graph topology.

** Keywords:** directed acyclic graph, Fourier analysis, binary systems of complex relations.

** UDC:** 530.16, 539.12.01

** PACS:** 04.60.Nc

** DOI:** 10.17238/issn2226-8812.2019.2.15-27

*Please cite this article in English as:*

Krugly A. L. The discrete model of spacetime and the binary pregeometry of Vladimirov. Space, Time and Fundamental Interactions, 2019, no. 2, pp. 15-27.