A formal analysis of Correspondence Theory

This paper provides a computational analysis of the complexity of GEN and Correspondence Theory in terms of the nature of the logic involved in their formulation. The first result of this analysis shows that the GEN function is not definable in Monadic Second Order (MSO) logic. Second, we show that the set of input-output Correspondence-theoretic candidates from a given underlying representation is definable in First Order (FO) logic, which is less complex than MSO-logic. Third, we present some case studies where the correct input-output Correspondence-theoretic candidate from a given underlying representation can be accomplished with FO-definable, language-specific, inviolable constraints without recourse to optimization.