8,393 research outputs found
On Descriptive Complexity, Language Complexity, and GB
We introduce , a monadic second-order language for reasoning about
trees which characterizes the strongly Context-Free Languages in the sense that
a set of finite trees is definable in iff it is (modulo a
projection) a Local Set---the set of derivation trees generated by a CFG. This
provides a flexible approach to establishing language-theoretic complexity
results for formalisms that are based on systems of well-formedness constraints
on trees. We demonstrate this technique by sketching two such results for
Government and Binding Theory. First, we show that {\em free-indexation\/}, the
mechanism assumed to mediate a variety of agreement and binding relationships
in GB, is not definable in and therefore not enforcible by CFGs.
Second, we show how, in spite of this limitation, a reasonably complete GB
account of English can be defined in . Consequently, the language
licensed by that account is strongly context-free. We illustrate some of the
issues involved in establishing this result by looking at the definition, in
, of chains. The limitations of this definition provide some insight
into the types of natural linguistic principles that correspond to higher
levels of language complexity. We close with some speculation on the possible
significance of these results for generative linguistics.Comment: To appear in Specifying Syntactic Structures, papers from the Logic,
Structures, and Syntax workshop, Amsterdam, Sept. 1994. LaTeX source with
nine included postscript figure
An Abstract Machine for Unification Grammars
This work describes the design and implementation of an abstract machine,
Amalia, for the linguistic formalism ALE, which is based on typed feature
structures. This formalism is one of the most widely accepted in computational
linguistics and has been used for designing grammars in various linguistic
theories, most notably HPSG. Amalia is composed of data structures and a set of
instructions, augmented by a compiler from the grammatical formalism to the
abstract instructions, and a (portable) interpreter of the abstract
instructions. The effect of each instruction is defined using a low-level
language that can be executed on ordinary hardware.
The advantages of the abstract machine approach are twofold. From a
theoretical point of view, the abstract machine gives a well-defined
operational semantics to the grammatical formalism. This ensures that grammars
specified using our system are endowed with well defined meaning. It enables,
for example, to formally verify the correctness of a compiler for HPSG, given
an independent definition. From a practical point of view, Amalia is the first
system that employs a direct compilation scheme for unification grammars that
are based on typed feature structures. The use of amalia results in a much
improved performance over existing systems.
In order to test the machine on a realistic application, we have developed a
small-scale, HPSG-based grammar for a fragment of the Hebrew language, using
Amalia as the development platform. This is the first application of HPSG to a
Semitic language.Comment: Doctoral Thesis, 96 pages, many postscript figures, uses pstricks,
pst-node, psfig, fullname and a macros fil
A hierarchy of mildly context sensitive dependency grammar
The paper presents Colored Multiplanar Link Grammars (CMLG). These grammars are reducible to extended right-linear S-grammars (Wartena 2001) where the storage type S is a concatenation of c pushdowns. The number of colors available in these grammars induces a hierarchy of Classes of CMLGs. By fixing also another parameter in CMLGs, namely the bound t for non-projectivity depth, we get c-Colored t-Non-projective Dependency Grammars (CNDG) that generate acyclic dependency graphs. Thus, CNDGs form a two-dimensional hier- archy of dependency grammars. A part of this hierarchy is mildly context-sensitive and non-projective.The paper presents Colored Multiplanar Link Grammars (CMLG). These grammars are reducible to extended right-linear S-grammars (Wartena 2001) where the storage type S is a concatenation of c pushdowns. The number of colors available in these grammars induces a hierarchy of Classes of CMLGs. By fixing also another parameter in CMLGs, namely the bound t for non-projectivity depth, we get c-Colored t-Non-projective Dependency Grammars (CNDG) that generate acyclic dependency graphs. Thus, CNDGs form a two-dimensional hier- archy of dependency grammars. A part of this hierarchy is mildly context-sensitive and non-projective.Peer reviewe
- …