Paper: Automatic Structures (at LICS 2000)
Authors: Achim Blumensath Erich GrädelAbstract
We study definability and complexity issues for automatic and omega-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover, they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical methods from finite structures to infinite ones.We explain the notion of (omega-) automatic structures, give examples, and discuss the relationship to automatic groups. We determine the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic. Further, we study closure properties and definability issues on automatic structures and present a technique for proving that a structure is not automatic. We give model-theoretic characterizations for automatic structures via interpretations. Finally, we discuss the composition theory of automatic structures and prove that they are closed under finitary Feferman-Vaught-like products.
BibTeX
@InProceedings{BlumensathGrdel-AutomaticStructures, author = {Achim Blumensath and Erich Grädel}, title = {Automatic Structures}, booktitle = {Proceedings of the Fifteenth Annual IEEE Symp. on Logic in Computer Science, {LICS} 2000}, year = 2000, editor = {Martin Abadi}, month = {June}, pages = {51--62}, location = {Santa Barbara, CA, USA}, publisher = {IEEE Computer Society Press} }