Abstract

Ehrenfeucht games are a useful tool in 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 it is shown that Graph Connectivity cannot be expressed by existential second-order formulas, where the second-order quantification is restricted to unary relations (Monadic NP), even in the presence of a built-in linear order. This settles an open problem from [1] and [11]. As a second application it is stated, that, on the other hand, the presence of a linear order increases the power of Monadic NP more than the presence of a successor relation. 1 Introduction Fagin [8] showed that the complexity class NP coincides with the class of all sets of finite structures that can be characterized by existential second-order formulas (\Sigma 1 1 ). Th...

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