Expressive power of monadic logics on words, trees, pictures, and graphs

We give a survey of the expressive power of various monadic logics on specific classes of finite labeled graphs, including words, trees, and pictures. Among the logics we consider, there are monadic secondorder logic and its existential fragment, the modal mu-calculus, and monadic least fixed-point logic. We focus on nesting-depth and quantifier alternation as a complexity measure of these logics.

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