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
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