Tree Adjoining Languages Research Articles

WMSO theories as grammar formalisms

We explore the use of weak monadic second-order languages over structures of varying dimension as specification languages for grammars and automata, focusing, in particular, on the extension of the longstanding results characterizing the regular and context-free languages in terms of definability in wS1S (one-dimensional) and wSnS (two-dimensional), respectively, to a characterization of the Tree-Adjoining Languages in terms of definability in the weak monadic second-order theory of certain three-dimensional tree-like structures. We then explore the application of these results to aspects of an existing large-scale Tree-Adjoining Grammar for English and close with some speculation on the feasibility of this approach as a means of building and maintaining such grammars.

Tabulation of Automata for Tree-Adjoining Languages

We propose a modular design of tabular parsing algorithms for tree- adjoining languages. The modularity is made possible by a separation of the parsing strategy from the mechanism of tabulation. The parsing strategy is expressed in terms of the construction of a nondeterministic automaton from a grammar; three distinct types of automaton will be discussed. The mechanism of tabulation leads to the simulation of these nondeterministic automata in polynomial time, independent of the parsing strategy. The proposed application of this work is the design of efficient parsing algorithms for tree-adjoining grammars and related formalisms.

TAL Recognition inO(M(n2)) Time

We propose anO(M(n2)) time algorithm for the recognition of tree adjoining languages (TALs), wherenis the size of the input string andM(k) is the time needed to multiply twok×kboolean matrices. Tree adjoining grammars are formalisms suitable for natural language processing and have received enormous attention in the past among not only natural language processing researchers but also algorithms designers. The first polynomial time algorithm for TAL parsing was proposed in 1986 and had a run time ofO(n6). Quite recently, anO(n3M(n)) algorithm has been proposed. The algorithm presented in this paper improves the run time of the recent result using an entirely different approach.

Tree-Adjoining Language Parsing in $O(n^6 )$ Time

In this paper, we present algorithms for parsing general tree-adjoining languages (TALs). Tree-adjoining grammars (TAGs) have been proposed as an elegant formalism for natural languages. It was an open question for the past ten years as to whether TAL parsing can be done in time $O(n^6 )$. We settle this question affirmatively by presenting an $O(n^3 M(n))$-time algorithm, where $M(k)$ is the time needed for multiplying two Boolean matrices of size $k \times k$ each. Since $O(k^{2.376} )$ is the current best-known value for $M(k)$, the time bound of our algorithm is $O(n^{5.376} )$. On an exclusive-read exclusive-write parallel random-access machine (EREW PRAM), our algorithm runs in time $O(n\log n)$ using ${{(n^2 M(n))} / {\log n}}$ processors. In comparison, the best-known previous parallel algorithm had a run time of $O(n)$ using $n^5 $ processors (on a systolic-array machine). We also present algorithms for parsing context-free languages (CFLs) and TALs whose worst-case run times are $O(n^3 )$ and $O(n^6 )$, respectively, but whose average run times are better. Therefore, these algorithms may be of practical interest.

An NC algorithm for recognizing tree adjoining languages

A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in natural language processing. This class of languages is known to properly include all context-free languages; for example, the noncontext-free sets {anbncn} and {ww} are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrent read, concurrent write parallel random-access machine (CRCW PRAM) inO(logn) time using polynomially many processors. Thus, the class of tree adjoining languages is inAC1 and hence inNC. This extends a previous result for context-free languages.

Chinese number-names, tree adjoining languages, and mild context-sensitivity

The Tree Adjoining Grammar formalism, both its single- as well as multiple-component versions, has recently received attention as a basis for the description and explication of natural language. We...