A Government-Binding Based Parser for Warlpiri, a Free-Word Order Language

Free-word order languages have long posed significant problems for standard parsing algorithms. This thesis presents an implemented parser, based on Government-Binding (GB) theory, for a particular free-word order language, Warlpiri, an aboriginal language of central Australia. The words in a sentence of a free-word order language may swap about relatively freely with little effect on meaning: the permutations of a sentence mean essentially the same thing. It is assumed that this similarity in meaning is directly reflected in the syntax. The parser presented here properly processes free word order because it assigns the same syntactic structure to the permutations of a single sentence. The parser also handles fixed word order, as well as other phenomena. On the view presented here, there is no such thing as a "configurational" or "non-configurational" language. Rather, there is a spectrum of languages that are more or less ordered. The operation of this parsing system is quite different in character from that of more traditional rule-based parsing systems, e.g., context-free parsers. In this system, parsing is carried out via the construction of two different structures, one encoding precedence information and one encoding hierarchical information. This bipartite representation is the key to handling both free- and fixed-order phenomena. This thesis first presents an overview of the portion of Warlpiri that can be parsed. Following this is a description of the linguistic theory on which the parser is based. The chapter after that describes the representations and algorithms of the parser. In conclusion, the parser is compared to related work. The appendix contains a substantial list of test cases ??th grammatical and ungrammatical ??at the parser has actually processed.

Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.