Algebraic Language

Let be an alphabet (i.e., a finite and nonempty set), and call its member letters. A word on is a finite sequence of letters , where . Denote the empty word by , and the set of all words in by . Define the concatenation (also called product) of a word with a word as . In general, concatenation is not commutative. Use the notation to mean the number of letters in the word . A language is then a subset of , and is said to be algebraic when a set of rewriting rules, applied recursively, forms all the words of and no others.