Polynomial operations and hierarchies of concatenation (in French)
Theoretical Computer Science
Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Partially-Ordered Two-Way Automata: A New Characterization of DA
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
Characterizing EF and EX tree logics
Theoretical Computer Science - Concurrency theory (CONCUR 2004)
Two-way unary temporal logic over trees
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Piecewise Testable Tree Languages
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Classifying discrete temporal properties
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Regular tree languages definable in FO
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
A Decidable Characterization of Locally Testable Tree Languages
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Algebra for Infinite Forests with an Application to the Temporal Logic EF
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
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 study tree languages that can be defined in Δ2. These are tree languages definable by a first-order formula whose quantifier prefix is $\exists^*\forall^*$, and simultaneously by a first-order formula whose quantifier prefix is $\forall^*\exists^*$, both formulas over the signature with the descendant relation. We provide an effective characterization of tree languages definable in Δ2. This characterization is in terms of algebraic equations. Over words, the class of word languages definable in Δ2forms a robust class, which was given an effective algebraic characterization by Pin and Weil [11].