Directed Reachability: From Ajtai-Fagin to Ehrenfeucht-Fraïssé Games

  title={Directed Reachability: From Ajtai-Fagin to Ehrenfeucht-Fra{\"i}ss{\'e} Games},
  author={Jerzy Marcinkowski},
In 1974 Ronald 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 9 ~ P, where ~ P is a tuple of relation symbols. and is a rst order formula. Fagin was also the rst to study monadic NP: the class of properties expressible by existential second order sentences where all quantiied relations are unary. In their very diicult paper AF90] Ajtai and Fagin show that directed… CONTINUE READING

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