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# Languages

## Definitions 1

An *alphabet* is a finite, nonempty set of symbols. We use
to denote this alphabet. *Note:* Symbols may be more than one English letter
long, e.g. **while** is a single symbol in Pascal.
A *string* is a finite sequence of symbols from .

The *length* of a string s, denoted |s|, is the number of symbols in it.

The *empty string* is the string of length zero.

It really looks like this:

but for convenience we usually write it like this:

denotes the set of all sequences of strings that are composed of zero or more
symbols of .

denotes the set of all sequences of strings composed of one or more symbols
of . That is,
=
- {}.

**A ***language* is a subset of .

Copyright © 1996 by David Matuszek

Last modified Jan 31, 1996