A1 Refereed original research article in a scientific journal
Undecidability in omega-regular languages
Authors: Halava V, Harju T, Karhumaki J
Publisher: IOS PRESS
Publication year: 2006
Journal:: Fundamenta Informaticae
Journal name in source: FUNDAMENTA INFORMATICAE
Journal acronym: FUND INFORM
Volume: 73
Issue: 1-2
First page : 119
Last page: 125
Number of pages: 7
ISSN: 0169-2968
Abstract
In the infinite Post Correspondence Problem an instance (h, g) consists of two morphisms h and 9, and the problem is to determine whether or not there exists an infinite word a such that h(alpha) = g(alpha). In the general case this problem was shown to be undecidable by K. Ruohonen (1985). Recently, it was proved that the infinite PCP is undecidable already when the domain alphabet of the morphisms consists of at least 9 letters. Here we show that the problem is undecidable for instances where the morphisms have a domain of 6 letters, when we restrict to solutions of omega-languages of the form R-omega where R is a given regular language.
In the infinite Post Correspondence Problem an instance (h, g) consists of two morphisms h and 9, and the problem is to determine whether or not there exists an infinite word a such that h(alpha) = g(alpha). In the general case this problem was shown to be undecidable by K. Ruohonen (1985). Recently, it was proved that the infinite PCP is undecidable already when the domain alphabet of the morphisms consists of at least 9 letters. Here we show that the problem is undecidable for instances where the morphisms have a domain of 6 letters, when we restrict to solutions of omega-languages of the form R-omega where R is a given regular language.
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