Algebraic Language

An algebraic language over an alphabet is a subset of whose words are exactly those formed by a set of recursively applied rewriting rules. Here, is a finite and nonempty set whose members are called letters. A word on is a finite sequence of letters , where . The empty word is denoted by , and the set of all words in by . The concatenation (also called product) of a word with a word is . In general, concatenation is not commutative. Use the notation to mean the number of letters in the word . A language is algebraic when the recursively applied rewriting rules form all the words of and no others.