In 1974 R. Fagin proved that properties of structures which are in NP are exactly the same as those expressible by existential second order sentences, that is sentences of the form...
in Structure'95. 14] R. Fagin. Easier ways to win logical games. In Proc. DIMACS Workshop on Descriptive Complexity and Finite Models, AMS 1997. 15] R. Fagin, L. Stockmeyer, M...