Handbook of theoretical computer science (vol. B)
Handbook of theoretical computer science (vol. B)
A New Logical Characterization of Büchi Automata
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
The Bounded Weak Monadic Quantifier Alternation Hierarchy of Equational Graphs Is Infinite
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
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Since the work of Rabin [9], it has been known that any monadic second order property of the (labeled) binary tree with successor functions (and not the prefix ordering) is a monadic Δ3 property. In this paper, we show this upper bound is optimal in the sense that there is a monadic Σ2 formula, stating the existence of a path where a given predicate holds infinitely often, which is not equivalent to any monadic II2 formula. We even show that some monadic second order definable properties of the binary tree are not definable by any boolean combination of monadic Σ2 and II2 formulas. These results rely in particular on applications of Ehrenfeucht-FraïssÉ like game techniques to the case of monadic Σ2 formulas.