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In words, the first condition says that the machine starts in the start state {{math|''q''<sub>0</sub>}}. The second condition says that given each character of string {{mvar|w}}, the machine will transition from state to state according to the transition function {{mvar|δ}}. The last condition says that the machine accepts {{mvar|w}} if the last input of {{mvar|w}} causes the machine to halt in one of the accepting states. Otherwise, it is said that the automaton ''rejects'' the string. The set of strings that {{mvar|M}} accepts is the [[Formal language|language]] ''recognized'' by {{mvar|M}} and this language is denoted by {{math|''L''(''M'')}}.
A deterministic finite automaton without accept states and without a starting state is known as a [[transition system]] or [[semiautomaton]].
For more comprehensive introduction of the formal definition see [[automata theory]].
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