Skip Navigation

Journal of Logic and Computation 2005 15(1):59-74; doi:10.1093/logcom/exh037
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Bluemnsath, A.
Right arrow Articles by Kreutzer, S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Vol. 15 No. 1, © The Author, 2005. Published by Oxford University Press. All rights reserved.

An Extension of Muchnik's Theorem

Achim Bluemnsath1 and Stephan Kreutzer2

1 Université Bordeaux-1, LaBRI, 351, Cours de la Liberation, 33405, Talence Cedex, France. E-mail: blume{at}labri.fr, 2 Humboldt-Universität zu Berlin, Institut für Informatik, Unter den Linden 6, 10099 Berlin, Germany. E-mail: Kreutzer{at}informatik.hu-berlin.de

One of the strongest decidability results in logic is the theorem of Muchnik which allows one to transfer the decidability of the monadic second-order theory of a structure to the decidability of the MSO-theory of its iteration, a tree built of disjoint copies of the original structure. We present a generalization of Muchnik's result to stronger logics, namely guarded second-order logic and its extensions by counting quantifiers. We also establish a strong equivalence result between monadic least fixed-point logic (M-LFP) and MSO on trees by showing that whenever M-LFP and MSO coincide on a structure they also coincide on its iteration.

Keywords: Monadic second-order logic, Muchnik's theorem, tree automata, fixed-point logics

Received 11 September 2003.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.