On Second-Order Monadic Monoidal and Groupoidal Quantifiers
Juha Kontinen, Heribert Vollmer · Logical Methods in Computer Science · 2010
We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers.