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Omega-regular Language





FORMAL DEFINITION

  • if ''A'' is a Regular Language , then ''A''ω is an omega-regular language

  • if ''A'' is a Regular Language , and ''B'' is an omega-regular language, then their Concatenation ''AB'' is an omega-regular language.(Note that ''BA'' is ''not'' well-defined.)

  • if ''A'', ''B'' are omega-regular languages, then their Intersection ''A''∩''B'', and Union ''A''∪''B'' are omega-regular.

  • if ''A'' is an omega-regular language, then so is its Complementω - ''A'').


Every omega-language is accepted by a nondeterministic Büchi Automaton ; the translation is constructive. An omega-language can also be described as an expression in Linear Temporal Logic (LTL).