Mathematics – Rings and Algebras
Scientific paper
2005-09-15
Mathematics
Rings and Algebras
19 pages
Scientific paper
We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which seem to be necessary to make the problem well-defined, the uniform word problem for semigroups described by automatic structures is decidable. Under the same conditions, we show that one can also decide whether the semigroup is completely simple or completely zero-simple; in the case that it is, one can compute a Rees matrix representation for the semigroup, in the form of a Rees matrix together with an automatic structure for its maximal subgroup. On the other hand, we show that it is undecidable in general whether a given element of a given automatic monoid has a right inverse.
Kambites Mark
Otto Friedrich
No associations
LandOfFree
Uniform decision problems in automatic semigroups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Uniform decision problems in automatic semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform decision problems in automatic semigroups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-407451