Decision problems for inverse monoids presented by a single sparse relator

Details Decision problems for inverse monoids presented by a single sparse relator Decision problems for inverse monoids presented by a single sparse relator

2009-11-08

arxiv.org/abs/0911.1484v1

Mathematics

Group Theory

Scientific paper

We study a class of inverse monoids of the form M = Inv< X | w=1 >, where the single relator w has a combinatorial property that we call sparse. For a sparse word w, we prove that the word problem for M is decidable. We also show that the set of words in (X \cup X^{-1})^* that represent the identity in M is a deterministic context free language, and that the set of geodesics in the Schutzenberger graph of the identity of M is a regular language.

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