Alternating automata on infinite trees
Theoretical Computer Science
Communication and concurrency
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Hierarchies of weak automata and weak monadic formulas
Theoretical Computer Science
Handbook of theoretical computer science (vol. B)
Handbook of theoretical computer science (vol. B)
Alternating automata, the weak monadic theory of trees and its complexity
Theoretical Computer Science
The modal mu-calculus alternation hierarchy is strict
Theoretical Computer Science
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
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Modeling concurrency by partial orders and nonlinear transition systems
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
Automata, tableaus and a reduction theorem for fixpoint calculi in arbitrary complete lattices
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Frame definability for classes of trees in the µ-calculus
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Description logic TBoxes: model-theoretic characterizations and rewritability
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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In 1970 [26], in Weakly definable relations and special automata, Math. Log. and Found. of Set Theory, pp 1-23, Rabin shows that a language is recognizable by a tree automaton with Büchi like infinitary condition if and only if it is definable as the projection of a weakly definable language. In this paper, we refine this result characterizing such languages as those definable in the monadic Σ2 level of the quantifier alternation depth hierarchy of monadic second order logic (MSO). This new result also contributes to a better understanding of the relationship between the quantifier alternation depth of hierarchy of MSO and the fixpoint alternation depth hierarchy of the mu-calculus: it shows that the bisimulation invariant fragment of the monadic Σ2 level equals the vµ-level of the mu-calculus hierarchy.