Corpus ID: 211252422

Extensions of $\omega$-Regular Languages.

  title={Extensions of \$\omega\$-Regular Languages.},
  author={Mikolaj Bojanczyk and Edon Kelmendi and Rafal Stefanski and Georg Zetzsche},
  journal={arXiv: Formal Languages and Automata Theory},
  • Mikolaj Bojanczyk, Edon Kelmendi, +1 author Georg Zetzsche
  • Published 2020
  • Mathematics, Computer Science
  • arXiv: Formal Languages and Automata Theory
  • We consider extensions of monadic second order logic over $\omega$-words, which are obtained by adding one language that is not $\omega$-regular. We show that if the added language $L$ has a neutral letter, then the resulting logic is necessarily undecidable. A corollary is that the $\omega$-regular languages are the only decidable Boolean-closed full trio over $\omega$-words. 

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