COMPUTER SYSTEMS AND NETWORKS

Pattern-dependent languages and fractal finite state automata for analysis elastic algorithms

A. S. Semenov

Moscow Aviation Institute (National Research University), Moscow, Russia

Abstract: To effectively solve the problem of developing elastic distributed algorithms that adapt to dynamic workloads and resource availability, a new elastic computational model based on pattern-dependent (PD) languages and their recognizers, fractal finite state automata (FFA), is introduced. The relationship between PD languages and geometric fractals is given. A method for designing elastic algorithms is proposed, which consists of two steps: first, extracting invariants from the algorithm by representing it as a chain of transforming multi-valued functions; and second, applying these invariants as operational symbols within the PD and FFA. The method is exemplified for developing an elastic algorithm for a binary tree based on the FFAs. This solution can be mapped onto an elastic computing network, where the nodes of the tree are implemented as servers or containers. Efficiency is achieved during the transition from simulation modeling to the development of a control system by minimizing additional transformations. The elastic computational model functions as the core of the control system, facilitating a more rapid and cost-efficient transition to practical system management. This advantage is supported by a comparative analysis presented in the paper, highlighting the proposed method's effectiveness and universality over the existing approaches.

Keywords: pattern dependent languages, fractal finite state automata, elastic algorithms, elastic computing.

Language: English

DOI: 10.14357/20718632250412

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