Equations over sets of natural numbers with addition only

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

15 Scopus citations

Abstract

Systems of equations of the form X = YZ and X = C are considered, in which the unknowns are sets of natural numbers, "+" denotes pairwise sum of sets S + T = {m + n | m ∈ S, n ∈ T}, and C is an ultimately periodic constant. It is shown that such systems are computationally universal, in the sense that for every recursive (r.e., co-r.e.) setS⊆ ℕ there exists a system with a unique (least, greatest) solution containing a component T with S = {n | 16n + 13 ∈ T}. This implies undecidability of basic properties of these equations. All results also apply to language equations over a one-letter alphabet with concatenation and regular constants.

Original languageEnglish
Title of host publicationSTACS 2009 - 26th International Symposium on Theoretical Aspects of Computer Science
Pages577-588
Number of pages12
StatePublished - 1 Dec 2009
Event26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009 - Freiburg, Germany
Duration: 26 Feb 200928 Feb 2009

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume3
ISSN (Print)1868-8969

Conference

Conference26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009
CountryGermany
CityFreiburg
Period26/02/0928/02/09

Scopus subject areas

  • Software

Cite this