Complexity of the Simpli ed Segmental Phonology

This article presents detailed complexity analysis of the encoding and decoding problems for the segmental phonology. The segmental model is a generative theory of phonological dependencies. As such, it poses two computational problems. The rst computational problem is the problem of actually encoding the dependencies of a given phonology into a given representation of phonological knowledge (the encoding problem). The second computational problem is the problem of deciding whether a given phonological representation encodes the dependencies of a given phonology (the decoding problem). We begin by proving that the encoding and decoding problems are both undecidable in the segmental model. Next, we motivate a simpli ed segmental model, that more accurately models the phonological dependencies actually proposed in the phonological literature. The simpli ed segmental model is a more restricted and more natural reformalization of the segmental model. To conclude, we prove that the encoding and decoding problems are NP-complete in this simpli ed segmental model. This paper was revised in May 1993 and submitted for journal publication. The author is particularly grateful to Morris Halle, Michael Kenstowicz, and an anonymous CL reviewer for their assistance and constructive criticisms. The author has been supported by a Young Investigator Award IRI-9258517 from the National Science