L(R)

In formal language theory and regular expressions, L(R) represents the language generated (or denoted) by the regular expression R. In other words, L(R) is the set of all strings that match the pattern described by the regular expression R.

Regular expressions are a concise way to describe patterns of strings. They consist of characters, metacharacters, and operators that specify the rules for matching strings. L(R) provides a formal interpretation of what a regular expression means, mapping the symbolic representation to the set of strings that it defines.

For instance, if R is the regular expression a*b, then L(R) is the set of all strings that consist of zero or more 'a' characters followed by a single 'b' character. This set can be written as {b, ab, aab, aaab, ...}.

Understanding L(R) is fundamental for working with regular expressions, as it allows one to reason about the precise set of strings that a given regular expression will match. The concept of L(R) is essential in areas such as compiler design, text processing, and network security where regular expressions are used extensively.