Handling equivalence classes of Optimality-Theoretic tableaux

Abstract

Many Optimality-Theoretic tableaux contain exactly the same information, and equivalence-preserving operations on them have been an object of study for some two decades. This paper shows that several of the operations proposed in the earlier literature together are actually enough to express any possible equivalence-preserving transformation. Moreover, every equivalence class of comparative tableaux (equivalently, of sets of Elementary Ranking Conditions, or ERC sets) has a unique and computable normal form that can be derived using those elementary operations in polynomial time. Any equivalence-preserving operation on comparative tableaux (ERC sets) is thus computable, and normal form tableaux may therefore represent their equivalence classes without loss of generality.