Automata in Chinese Remainder Theorem - Dutta, Mridul; Saikia, Helen K. (Communications in Mathematics and Applications, 2022)
. Automaton is a system that spontaneously gives an output from an input. The input may be energy, information, materials, etc. The system works without the intervention of man. Simply automaton (plural: automata or automatons) is a self–operating machine. Its synonym is ROBOT. In this paper, an attempt has been made to exhibit the relation between linear congruence and automata theory. Also, an effort has been put to solve certain problems of the Chinese Remainder theorem using the Cartesian product of finite automata theory. In deterministic finite automata, the acceptable strings give the solutions of the Chinese Remainder Theorem (CRT). The main result of the paper is that residue classes can be recognized by finite automaton. This is the novelty of the article. Finally, we conclude with certain examples and non-examples alike!