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.
See alsoDyck Language
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ReferencesBousquet-Mélou, M. "Convex Polyominoes and Algebraic Languages." J. Phys. A: Math. Gen. 25, 1935-1944, 1992.Delest, M.-P. and Viennot, G. "Algebraic Languages and Polyominoes [sic] Enumeration." Theoret. Comput. Sci. 34, 169-206, 1984.
Referenced on Wolfram|AlphaAlgebraic Language
Cite this as:
Weisstein, Eric W. "Algebraic Language." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlgebraicLanguage.html