Abstract
It is shown that membership in rational subsets of wreath products H ≀ V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product ℤ ≀ ℤ with an undecidable membership problem.
This work was supported by the DAAD research project RatGroup. The second author was partially supported by a grant from the Simons Foundation (#245268 to Benjamin Steinberg). Omitted proofs can be found in the long version [24] of this paper.
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Lohrey, M., Steinberg, B., Zetzsche, G. (2013). Rational Subsets and Submonoids of Wreath Products. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_33
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