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Title:Correspondence Theory: More Candidates Than Atoms in the Universe
Authors:Markus Walther
Comment:first appeared as tech report MAL-6 in http://www.uni-marburg.de/linguistik/mal
Abstract:In Correspondence Theory (McCarthy and Prince 1995), elements of two strings (S1, S2) belonging to designated representational
levels such as (input, output) may become associated through an arbitrary correspondence relation, while constraints like MAX, DEP
evaluate such string pairs relative to the set of elementwise correspondences they find. Using some elementary calculations, I show
that the number of candidates produced by correspondence-theoretic GEN quickly grows out of proportion, exceeding the estimated
amount of atoms in the entire universe for strings S1 of length greater 6 under conservative upper bounds for amount of epenthesis,
reduplication and allophonic inventory size. This finding suggests that it is hopeless to do realistic manual verification of
correspondence-theoretic analyses, while leaving open suitable restrictions of the formal power of correspondence, as e.g. proposed
by Primitive Optimality Theory (Eisner 1997). While phonology may not count, phonologists clearly should sometimes.
Type:Paper/tech report
Area/Keywords:Formal Analysis,Computation,Phonology
Article:Version 1