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 maybe energy, information, materials, etc. The system works without the intervention of man. Simplyautomaton (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 andautomata theory. Also, an effort has been put to solve certain problems of the Chinese Remaindertheorem using the Cartesian product of finite automata theory. In deterministic finite automata, theacceptable strings give the solutions of the Chinese Remainder Theorem (CRT). The main result of thepaper 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!
Keywords: Automata; Cartesian product of DFA; Chinese Remainder Theorem