Context-Free Graph Properties via Definable Decompositions

Monadic-second order logic (mso-logic) is successfully applied in both language theory and algorithm design. In the former, properties definable by mso-formulas are exactly the regular properties on many structures like, most prominently, strings. In the latter, solving a problem for structures of bounded tree width is routinely done by defining it in terms of an mso-formula and applying general formula-evaluation procedures like Courcelle’s. The present paper furthers the study of second-order logics with close connections to language theory and algorithm design