Literal shuffle on $\omega$-languages(Semigroups, Formal Languages and Computer Systems)
Tetsuo Moriya, Hideki Yamasaki · Kyoto University Research Information Repository (Kyoto University) · 1996
We consider literal shuffle on $\omega$ -languages.First, we show that a duo (a family of $\omega$ -languages closed under $\epsilon$ -free lnorphisn\iota s and $\mathrm{i}_{1}\iota \mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{e}$ $\epsilon$ -free $\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{l}\iota \mathrm{i}\mathrm{s}\mathrm{n}\iota \mathrm{s}$ ) is closed under literal $\mathrm{s}\mathrm{l}\downarrow \mathrm{u}\mathrm{f}\mathfrak{l}\mathrm{l}\mathrm{e}$ if and only if it is closed under intersection.Next we investigate the closure properties of solne classes of tlle $\omega$ -regular languages under literal shuffle and slruffle.Last the relation between literal shuffle altd shuffle are presented.