AMAR: A Computational Model of Autosegmental Phonology

This report describes a computational system with which phonologists may describe a natural language in terms of autosegmental phonology, currently the most advanced theory pertaining to the sound systems of human languages. This system allows linguists to easily test autosegmental hypotheses against a large corpus of data. The system was designed primarily with tonal systems in mind, but also provides support for tree or feature matrix representation of phonemes (as in The Sound Pattern of English), as well as syllable structures and other aspects of phonological theory. Underspecification is allowed, and trees may be specified before, during, and after rule application. The association convention is automatically applied, and other principles such as the conjunctivity condition are supported. The method of representation was designed such that rules are designated in as close a fashion as possible to the existing conventions of autosegmental theory while adhering to a textual constraint for maximum portability.

Computational Structure of GPSG Models: Revised Generalized Phrase Structure Grammar

The primary goal of this report is to demonstrate how considerations from computational complexity theory can inform grammatical theorizing. To this end, generalized phrase structure grammar (GPSG) linguistic theory is revised so that its power more closely matches the limited ability of an ideal speaker--hearer: GPSG Recognition is EXP-POLY time hard, while Revised GPSG Recognition is NP-complete. A second goal is to provide a theoretical framework within which to better understand the wide range of existing GPSG models, embodied in formal definitions as well as in implemented computer programs. A grammar for English and an informal explanation of the GPSG/RGPSG syntactic features are included in appendices.

Computational Structure of Human Language

The central thesis of this report is that human language is NP-complete. That is, the process of comprehending and producing utterances is bounded above by the class NP, and below by NP-hardness. This constructive complexity thesis has two empirical consequences. The first is to predict that a linguistic theory outside NP is unnaturally powerful. The second is to predict that a linguistic theory easier than NP-hard is descriptively inadequate. To prove the lower bound, I show that the following three subproblems of language comprehension are all NP-hard: decide whether a given sound is possible sound of a given language; disambiguate a sequence of words; and compute the antecedents of pronouns. The proofs are based directly on the empirical facts of the language user's knowledge, under an appropriate idealization. Therefore, they are invariant across linguistic theories. (For this reason, no knowledge of linguistic theory is needed to understand the proofs, only knowledge of English.) To illustrate the usefulness of the upper bound, I show that two widely-accepted analyses of the language user's knowledge (of syntactic ellipsis and phonological dependencies) lead to complexity outside of NP (PSPACE-hard and Undecidable, respectively). Next, guided by the complexity proofs, I construct alternate linguisitic analyses that are strictly superior on descriptive grounds, as well as being less complex computationally (in NP). The report also presents a new framework for linguistic theorizing, that resolves important puzzles in generative linguistics, and guides the mathematical investigation of human language.