2007.29: Uniform decision problems for automatic semigrouos
2007.29: Mark Kambites and Friedrich Otto (2006) Uniform decision problems for automatic semigrouos. Journal of Algebra, 303 (2). pp. 789-809. ISSN 0021-8669
Full text available as:
|PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
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 are 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.
|Subjects:||MSC 2000 > 18 Category theory; homological algebra|
|Deposited By:||Miss Louise Stait|
|Deposited On:||27 March 2007|