0, 1, 00, 01, 10, 11, 000, etc. are all in the Kleene closure of the alphabet (where ε represents the empty string). Applications Alphabets are important in the use of formal languages, automata and semiautomata. In most cases, for defining instances of automata, such as deterministic finite automata (DFAs), it is required to specify an alphabet from which the input strings for the automaton are built. In these applications, an alphabet is usually required to be a finite set, but is not otherwise restricted. When using automata, regular expressions, or formal grammars as part of string-processing algorithms, the alphabet may be assumed to be the character set of the text to be processed by these algorithms, or a subset of allowable characters from the character set. See also Combinatorics on words References Literature John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley Publishing, Reading Massachusetts, 1979. . Formal languages Combinatorics on words