The Closure of Monadic NP

The Closure of Monadic NP

It is a well-known result of Fagin that the complexity class NP coincides with the class of problems expressible in existential second-order logic (Z i), which allows sentences consisting of a string of existential second-order quantifiers followed by a first-order formula. Monadic NP is the class of problems expressible in monadic Z ; , i.e., Z ; with the restriction that the second-order quan...

On Monadic NP vs. Monadic co-NP

It is a well-known result of Fagin that the complexity class NP coincides with the class of problems expressible in existential second-order logic (1 ;). Monadic NP is the class of problems expressible in monadic Z;, i.e., 1: with the restriction that the second-order quantifiers range only over sets (as opposed to ranging over, say, binary relations). We prove that connectivity of finite graph...

Monadische Erweiterungen von monadic NP

Graph Connectivity and Monadic NP

product of the permutations of G 0 is not an n-cycle, hence G 0 is not connected. We have to show, nally, that Duplicator has a winning strategy in the k-round FO Ehrenfeucht game on G and G 0. For every q, we write H q for the subgraph of G, induced by the middle two columns of vertices of the subgraph L i q j i q. Accordingly we deene the subgraphs H 0 q of G 0. j) for i 6 = j; (i) follows fr...

Graph Connectivity and Monadic NP

Ehrenfeucht games are a useful tool an proving that certain properties of finite structures are not expressible by formulas of a certain type. In this paper a new method is introduced that allows the extension of a local winning strategy for Duplicator, one of the two players in Ehrenfeucht games, to a global winning strategy. As an application i t i s shown that Graph Connectivity cannot be ex...