Some results on equational unification
CADE-10 Proceedings of the tenth international conference on Automated deduction
Vertex-transitive graphs and accessibility
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Theoretical Computer Science
The Book of Traces
Monadic second-order logic on tree-like structures
Theoretical Computer Science
Semi-Groups Acting on Context-Free Graphs
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
A Short Introduction to Infinite Automata
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Tree-partite graphs and the complexity of algorithms
FCT '85 Fundamentals of Computation Theory
Automatic Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Decidability and complexity in automatic monoids
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
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We prove that a connected graph of bounded degree with only finitely many orbits has a decidable MSO-theory if and only if it is context-free. This implies that a group is context-free if and only if its Cayley-graph has a decidable MSO-theory. On the other hand, the first-order theory of the Cayley-graph of a group is decidable if and only if the group has a decidable word problem. For Cayley-graphs of monoids we prove the following closure properties. The class of monoids whose Cayley-graphs have decidable MSO-theories is closed under free products. The class of monoids whose Cayley-graphs have decidable first-order theories is closed under general graph products. For the latter result on first-order theories we introduce a new unfolding construction, the factorized unfolding, that generalizes the tree-like structures considered by Walukiewicz. We show and use that it preserves the decidability of the first-order theory.Most of the proofs are omitted in this paper, they can be found in the full version [17].