Automatas

Automatas, also called automata, are abstract computational devices used to model and analyze computation and formal languages. They consist of a finite set of states, an input alphabet, a transition function, a start state, and a set of accepting states. Depending on determinism of the transition function, automata are classified as deterministic or nondeterministic.

Several canonical models are studied: finite automata (FAs) process finite strings and recognize regular languages; deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs) are equivalent in expressive power, though NFAs can be more compact. Pushdown automata (PDAs) extend finite automata with a stack and recognize context-free languages. Linear-bounded automata and Turing machines are more powerful models capable of recognizing a broad class of recursively enumerable languages. Cellular automata are parallel, discrete systems with vast state spaces that evolve in discrete time steps according to local rules.

Automata provide a formal link to formal languages. A language is regular if it can be recognized by a finite automaton; context-free if recognized by a pushdown automaton; more complex languages require machines like Turing machines. These correspondences are part of the Chomsky hierarchy. The equivalence of DFAs and NFAs is a foundational result; regular expressions describe the same class of languages as finite automata.

Applications include lexical analysis and compilation, text search algorithms, protocol verification, model checking, and the design of digital circuits. Automata theory also informs areas such as formal verification and computational complexity.

History: the theory originated in the 1950s with work by Kleene and others, later expanded with Noam Chomsky's hierarchy and Turing's machine as a general model of computation. Today automata remain a core tool in theoretical computer science and related disciplines.