Complexity classes and theories of finite models

AbstractLetL $$ \subseteq $$ Σ* be accepted in timef(n) by a nondeterministic Turing machine. Then there is a monadic existential second-order sentence σ in the language of + such that for everyx∈Σ*,x∈L if and only if a certain structureUxf of cardinalityf(|x|) satisfies σ. It follows that ifL is accepted in nondeterministic timend, d a natural number, then there is a sentence whose relational symbols ared-ary or less, whose finite spectrum isL.

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