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omega language : ウィキペディア英語版
omega language

An ω-language is a set of infinite-length sequences of symbols.
==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 → Σ, with the value at ''i'' giving the symbol at position ''i''. The infinite words, or ω-words, can likewise be viewed as functions from \mathbb to Σ. 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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