Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
On the regular structure of prefix rewriting
CAAP '90 Selected papers of the conference on Fifteenth colloquium on trees in algebra and programming
Monadic second-order definable graph transductions: a survey
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Languages, automata, and logic
Handbook of formal languages, vol. 3
Automata, Boolean matrices, and ultimate periodicity
Information and Computation
Monadic second-order logic on tree-like structures
Theoretical Computer Science
The monadic theory of morphic infinite words and generalizations
Information and Computation
On infinite transition graphs having a decidable monadic theory
Theoretical Computer Science
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Decidability of the Theory of the Totally Unbounded "-Layered Structure
TIME '04 Proceedings of the 11th International Symposium on Temporal Representation and Reasoning
Higher order pushdown automata, the Caucal hierarchy of graphs and parity games
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Decidability of MSO theories of tree structures
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Decidability of MSO theories of tree structures
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
| Hi-index | 0.00 |
In this paper we provide an automaton-based solution to the decision problem for a large set of monadic second-order theories of deterministic tree structures. We achieve it in two steps: first, we reduce the considered problem to the problem of determining, for any Rabin tree automaton, whether it accepts a given tree; then, we exploit a suitable notion of tree equivalence to reduce (a number of instances of ) the latter problem to the decidable case of regular trees. We prove that such a reduction works for a large class of trees, that we call residually regular trees. We conclude the paper with a short discussion of related work.