Automata and Computability

Automata and computability explore how machines and algorithms solve problems. Automata are abstract models of computation, like simple "machines" that process input (such as strings of symbols) to recognize patterns or make decisions. Computability studies which problems can be solved logically—some are solvable, some are fundamentally impossible due to their complexity or nature. Together, they help us understand the limits of what computers can do and how to design algorithms that solve real-world tasks efficiently or recognize when a problem exceeds computational capabilities.