Language equations are mathematical statements that resemble numerical equations

Equation

An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

, but the variables assume values of formal languages rather than numbers. Instead of arithmetic operations in numerical equations, the variables are joined by language operations. Among the most common operations on two languages A and B are the set union A ∪ B, the set intersection A ∩ B, and the concatenation A⋅B. Finally, as an operation taking a single operand

Operand

In mathematics, an operand is the object of a mathematical operation, a quantity on which an operation is performed.-Example :The following arithmetic expression shows an example of operators and operands:3 + 6 = 9\;...

, the set A^* denotes the Kleene star

Kleene star

In mathematical logic and computer science, the Kleene star is a unary operation, either on sets of strings or on sets of symbols or characters. The application of the Kleene star to a set V is written as V*...

 of the language A. Therefore language equations can be used to represent formal grammar

Formal grammar

A formal grammar is a set of formation rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax...

s, since the languages generated by the grammar must be the solution of a system of language equations.

External links

• Workshop on Theory and Applications of Language Equations (TALE 2007)
• Language equations