Abstract
We incorporate finite monoids into the theory of Rabin recognizability of infinite tree languages. We define a free monoid of infinite trees and associate with each infinite tree language L a language L of infinite words over this monoid. Using this correspondence we introduce strong monoid recognizability of infinite tree languages (strengthening the standard notion for infinite words) and show that it is equivalent to Rabin recognizability. We also show that there exists an infinite tree language L which is not Rabin recognizable, but its associated language L is monoid recognizable (in the standard sense). Our positive result opens the theory of varieties of infinite tree languages, extending those for finite and infinite words and finite trees.
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Beauquier, D., Podelski, A. (1993). Rabin tree automata and finite monoids. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_18
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DOI: https://doi.org/10.1007/3-540-57182-5_18
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