Automatic structures: overview and future directions
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Automatic Presentations for Cancellative Semigroups
Language and Automata Theory and Applications
Automatic presentations for semigroups
Information and Computation
Model theoretic complexity of automatic structures
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Fundamenta Informaticae
An undecidable property of context-free linear orders
Information Processing Letters
First-order and counting theories of ω-automatic structures
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Automatic presentations for finitely generated groups
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Hausdorff rank of scattered context-free linear orders
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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We investigate partial orders that are computable, in a precisesense, by finite automata. Our emphasis is on treesand linear orders. We study the relationship between automaticlinear orders and trees in terms of rank functions thatare versions of Cantor-Bendixson rank. We prove that automaticlinear orders and automatic trees have finite rank.As an application we provide a procedure for deciding theisomorphism problem for automatic ordinals. We also investigatethe complexity and definability of infinite paths inautomatic trees. In particular, we show that every infinitepath in an automatic tree with countably many infinite pathsis a regular language.