Abstract
For a languageL the syntactic monoid SynL is trivial if and only if indeedL itself is trivial, that isL = Ø orL=X*. As a surprise one realizes that the syntactic monoid SynL of an ω-languageL being trivial by no means implies thatL be trivial. This situation is analyzed in this paper. The results may help clarify the difference between deterministically and nondeterministically finite state acceptable ω-languages.
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References
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This research was supported in part by Grant A7877 of the Natural Sciences and Engineering Research Council of Canada and partly also by Deutsche Forschungsgemeinschaft.
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Jürgensen, H., Thierrin, G. Onω-Languages whose syntactic monoid is trivial. International Journal of Computer and Information Sciences 12, 359–365 (1983). https://doi.org/10.1007/BF01008047
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DOI: https://doi.org/10.1007/BF01008047