International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Alternating automata, the weak monadic theory of trees and its complexity
Theoretical Computer Science
Modal Logic over Finite Structures
Journal of Logic, Language and Information
Automata for the Modal mu-Calculus and related Results
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Monadic Second Order Logic on Tree-Like Structures
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
On the Semantics of Fair Parallelism
Proceedings of the Abstract Software Specifications, 1979 Copenhagen Winter School
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Characterizing EF over infinite trees and modal logic on transitive graphs
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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We provide a characterization theorem, in the style of van Ben them and Janin-Walukiewicz, for the alternation-free fragment of the modal mu-calculus. For this purpose we introduce a variant of standard monadic second-order logic (MSO), which we call well-founded monadic second-order logic (WFMSO). When interpreted in a tree model, the second-order quantifiers of WFMSO range over subsets of conversely well-founded sub trees. The first main result of the paper states that the expressive power of WFMSO over trees exactly corresponds to that of weak MSO-automata. Using this automata-theoretic characterization, we then show that, over the class of all transition structures, the bisimulation-invariant fragment of WFMSO is the alternation-free fragment of the modal mu-calculus. As a corollary, we find that the logics WFMSO and WMSO (weak monadic second-order logic, where second-order quantification concerns finite subsets), are incomparable in expressive power.