Optimality Theory (OT), introduced by Alan Prince and Paul Smolensky in 1993, fundamentally reconceived phonological grammar. Rather than viewing phonology as a derivation that transforms underlying forms through ordered rules, OT models it as an optimization problem. A generator function (GEN) produces the universe of possible output candidates for a given input, and an evaluator function (EVAL) selects the optimal candidate — the one that best satisfies a ranked set of violable constraints. The key innovation is that constraints are violable: all candidates violate some constraints, and the grammar selects the candidate with the least serious violations according to the language-specific ranking.
The OT Architecture
GEN: produces candidate set {c₁, c₂, c₃, ...}
CON: universal constraint set {C₁, C₂, C₃, ...}
EVAL: ranking C₁ >> C₂ >> C₃ >> ...
Optimal output = candidate that incurs the least
serious violations under strict domination:
c₁ > c₂ iff at the highest-ranked constraint where
c₁ and c₂ differ, c₁ has fewer violations
OT's core principle is strict domination: a single violation of a higher-ranked constraint is worse than any number of violations of lower-ranked constraints. This makes evaluation tractable — candidates can be compared by examining constraints in order from highest to lowest ranked, eliminating candidates at each step. Languages differ not in their constraints (which are universal) but in their rankings. The factorial typology — the set of possible languages generated by all permutations of constraint rankings — predicts which phonological systems are humanly possible.
Computational Properties
The computational complexity of OT has been extensively studied. If GEN produces a finite candidate set, evaluation is polynomial in the number of candidates and constraints. However, the standard assumption that GEN is unrestricted (producing infinitely many candidates) raises questions about how EVAL identifies the optimum efficiently. Ellison (1994) and Eisner (2000) showed that when constraints and GEN can be expressed as finite-state transducers, the optimal candidate can be computed using finite-state composition and shortest-path algorithms. This finite-state OT framework makes the theory computationally implementable.
A central computational question in OT is how learners acquire the correct constraint ranking from observed data. Tesar and Smolensky (2000) proposed the Constraint Demotion algorithm, which learns a ranking consistent with a set of winner-loser pairs: if the learner's current ranking selects the wrong output, the constraints favoring the wrong candidate are demoted below those favoring the correct one. The Gradual Learning Algorithm (Boersma, 1997) extends this to stochastic OT, where constraints have continuous ranking values with noise, allowing it to model variation and gradient acceptability judgments.
Extensions and Criticisms
Numerous extensions of OT have been proposed. Harmonic Grammar replaces strict domination with weighted constraint combination, where each constraint has a numerical weight and the optimal candidate minimizes the weighted sum of violations. Stochastic OT adds noise to ranking values, generating probabilistic predictions. Correspondence Theory (McCarthy and Prince, 1995) enriches the constraint set with faithfulness constraints that penalize differences between input and output, allowing OT to handle the full range of phonological processes including deletion, insertion, and metathesis.
Critics of OT have questioned the richness of GEN (which must generate candidates with arbitrary modifications), the lack of intermediate representations, and the difficulty of accounting for phonological opacity — cases where surface-true generalizations are violated because of interactions with other processes. Despite these debates, OT remains the dominant framework in theoretical phonology and continues to inspire computational work on constraint-based grammar.