The Complexity of Phonology

The application of complexity theory to natural language grammars over the past two decades is shown to include two arguments incorrectly claiming that particular theoretical formalisms cannot characterize human phonology as they incur nondeterministic polynomial (NP) hardness, ie, an intractable increase in computational steps as problem size increases. Both the conclusion of G. Edward Barton (1986) that two-level phonology & morphology systems cannot match human analytic & generative ability & the similar conclusions of William J. Idsardi that optimality theory is intractably complex invoke an unrestrained increase in problem size that depends on asymptotic analysis. Granting that the models in question incur NP hardness, the problems that call for them -- harmony rules for Barton & self-conjoined constraints for Idsardi -- are limited by the finite, small inventories of features & phonemes of all natural languages. Asymptotic analysis is irrelevant in a domain where problems cannot become arbitrarily large, & Kolmogorov complexity -- the length of the shortest program that generates a given object -- is suggested as an alternative tool to evaluate formal grammars. J. Hitchcock