The hierarchy inside closed monadic Σ1 collapses on the infinite binary tree
نویسندگان
چکیده
Closed monadic Σ1, as proposed in [AFS98], is the existential monadic second order logic where alternation between existential second order quantifiers and first order quantifiers is allowed. Despite some effort very little is known about the expressive power of this logic on finite structures. We construct a tree automaton which exactly characterizes closed monadic Σ1 on the Rabin tree and give a full analysis of the expressive power of closed monadic Σ1 in this context. In particular, we prove that the hierarchy inside closed monadic Σ1, defined by the number of alternations between blocks of first order quantifiers and blocks of existential second order quantifiers collapses, on the infinite tree, to the
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