Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Automata, Languages, and Machines
Automata, Languages, and Machines
Word Processing in Groups
Rational Graphs Trace Context-Sensitive Languages
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Languages Defined by Higher Type Program Schemes
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
On Infinite Transition Graphs Having a Decidable Monadic Theory
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
A Short Introduction to Infinite Automata
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Automatic Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
The composition method
Automatic linear orders and trees
ACM Transactions on Computational Logic (TOCL)
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Rational graphs are a family of graphs defined using labelled rational transducers. Unlike automatic graphs (defined using synchronized transducers) the first order theory of these graphs is undecidable, there is even a rational graph with an undecidable first order theory. In this paper we consider the family of rational trees, that is rational graphs which are trees. We prove that first order theory is decidable for this family. We also present counter examples showing that this result cannot be significantly extended both in terms of logic and of structure.