Titlebook: Automata, Languages, and Programming; 41st International C Javier Esparza,Pierre Fraigniaud,Elias Koutsoupias Conference proceedings 2014 S

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Weak , with Path Quantifiers over Infinite TreesThis paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier . and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automaton model is decided using profinite trees.

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Piecewise Boolean Algebras and Their DomainsWe characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise Boolean domains equipped with an orientation, or as full structure sheaves on piecewise Boolean domains.

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