Formal Definition
Let Σ be a set of symbols (not necessarily finite). Following the standard definition from formal language theory, Σ* is the set of all finite words over Σ. Every finite word has a length, which is, obviously, a natural number. Given a word w of length n, w can be viewed as a function from the set {0,1,...,n-1} → Σ. The infinite words, or ω-words, can likewise be viewed as functions from to Σ, with the value at i giving the symbol at position i. The set of all infinite words over Σ is denoted Σω. The set of all finite and infinite words over Σ is sometimes written Σ∞.
Thus, an ω-language L over Σ is a subset of Σω.
Read more about this topic: Omega Language
Famous quotes containing the words formal and/or definition:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)