Please use this identifier to cite or link to this item:
|Title:||Index sets and universal numberings||Authors:||Jain, S.
|Issue Date:||2009||Citation:||Jain, S.,Stephan, F.,Teutsch, J. (2009). Index sets and universal numberings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 5635 LNCS : 270-279. ScholarBank@NUS Repository. https://doi.org/10.1007/978-3-642-03073-4_28||Abstract:||This paper studies the Turing degrees of various properties defined for universal numberings, that is, for numberings which list all partial-recursive functions. In particular properties relating to the domain of the corresponding functions are investigated like the set DEQ of all pairs of indices of functions with the same domain, the set DMIN of all minimal indices of sets and DMIN 1 of all indices which are minimal with respect to equality of the domain modulo finitely many differences. A partial solution to a question of Schaefer is obtained by showing that for every universal numbering with the Kolmogorov property, the set DMIN1 is Turing equivalent to the double jump of the halting problem. Furthermore, it is shown that the join of DEQ and the halting problem is Turing equivalent to the jump of the halting problem and that there are numberings for which DEQ itself has 1-generic Turing degree. © 2009 Springer Berlin Heidelberg.||Source Title:||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)||URI:||http://scholarbank.nus.edu.sg/handle/10635/113936||ISBN:||3642030726||ISSN:||03029743||DOI:||10.1007/978-3-642-03073-4_28|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Oct 20, 2021
checked on Oct 14, 2021
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.