First-order logic and star-free sets
Journal of Computer and System Sciences
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Hierarchies of weak monadic formulas for two successors arithmetic
Journal of Information Processing and Cybernetics
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
On the Structure of the Monadic Logic of the Binary Tree
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
On Infinite Transition Graphs Having a Decidable Monadic Theory
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
A hierarchy of sets of infinite trees
Proceedings of the 6th GI-Conference on Theoretical Computer Science
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Here we deal with the question of definability of infinite graphs up to isomorphism by weak monadic second-order formulæ. In this respect, we prove that the quantifier alternation bounded hierarchy of equational graphs is infinite. Two proofs are given: the first one is based on the Ehrenfeucht-FraissÉ games; the second one uses the arithmetical hierarchy. Next, we give a new proof of the Thomas's result according to which the bounded hierarchy of the weak monadic second-order logic of the complete binary tree is infinite.