Finite Automaton
An abstract machine with finitely many states and transitions that reads an input string symbol by symbol and ends in acceptance or rejection.
A finite automaton limits its memory to a finite set of states. The standard model is described by the state set Q, alphabet Σ, transition function δ, initial state q0, and accepting states F.
A deterministic automaton has one next state for each state-symbol pair. A nondeterministic automaton can admit several alternatives; despite that difference, DFA and NFA recognize the same class of regular languages.
The language of the automaton is the set of strings that take the machine from its initial state to an accepting state. See Right-Linear Grammar for the grammar view and Automata Theory and Formal Languages for the broader progression.