Automata presenting structures: A survey of the finite string case

Bulletin of Symbolic Logic 14 (2):169-209 (2008)
Abstract
A structure has a (finite-string) automatic presentation if the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability
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DOI 10.2178/bsl/1208442827
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References found in this work BETA
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Definability Hierarchies of General Quantifiers.L. Hella - 1989 - Annals of Pure and Applied Logic 43 (3):235.

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Citations of this work BETA
Some Natural Decision Problems in Automatic Graphs.Dietrich Kuske & Markus Lohrey - 2010 - Journal of Symbolic Logic 75 (2):678-710.
Automatic Structures of Bounded Degree Revisited.Dietrich Kuske & Markus Lohrey - 2011 - Journal of Symbolic Logic 76 (4):1352-1380.
Automatic Models of First Order Theories.Pavel Semukhin & Frank Stephan - 2013 - Annals of Pure and Applied Logic 164 (9):837-854.
The Isomorphism Problem for Ω-Automatic Trees.Dietrich Kuske, Jiamou Liu & Markus Lohrey - 2013 - Annals of Pure and Applied Logic 164 (1):30-48.
A Hierarchy of Tree-Automatic Structures.Olivier Finkel & Stevo Todorčević - 2012 - Journal of Symbolic Logic 77 (1):350-368.

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