2,809 research outputs found
Expressing Context-Free Tree Languages by Regular Tree Grammars
In this thesis, three methods are investigated to express context-free tree languages by regular tree grammars. The first method is a characterization. We show restrictions to context-free tree grammars such that, for each restricted context-free tree grammar, a regular tree grammar can be constructed that induces the same tree language. The other two methods are approximations. An arbitrary context-free tree language can be approximated by a regular tree grammar with a restricted pushdown storage. Furthermore, we approximate weighted context-free tree languages, induced by weighted linear nondeleting context-free tree grammars, by showing how to approximate optimal weights for weighted regular tree grammars
Two characterisation results of multiple context-free grammars and their application to parsing
In the first part of this thesis, a Chomsky-SchĂĽtzenberger characterisation and an automaton characterisation of multiple context-free grammars are proved. Furthermore, a framework for approximation of automata with storage is described. The second part develops each of the three theoretical results into a parsing algorithm
Practical experiments with regular approximation of context-free languages
Several methods are discussed that construct a finite automaton given a
context-free grammar, including both methods that lead to subsets and those
that lead to supersets of the original context-free language. Some of these
methods of regular approximation are new, and some others are presented here in
a more refined form with respect to existing literature. Practical experiments
with the different methods of regular approximation are performed for
spoken-language input: hypotheses from a speech recognizer are filtered through
a finite automaton.Comment: 28 pages. To appear in Computational Linguistics 26(1), March 200
Controlled non uniform random generation of decomposable structures
Consider a class of decomposable combinatorial structures, using different
types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the
random generation of such structures with respect to a size and a targeted
distribution in of its \emph{distinguished} atoms. We consider two
variations on this problem. In the first alternative, the targeted distribution
is given by real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 <
\TargFreq_i < 1 for all and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We
aim to generate random structures among the whole set of structures of a given
size , in such a way that the {\em expected} frequency of any distinguished
atom \At_i equals \TargFreq_i. We address this problem by weighting the
atoms with a -tuple \Weights of real-valued weights, inducing a weighted
distribution over the set of structures of size . We first adapt the
classical recursive random generation scheme into an algorithm taking
\bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw structures from
the \Weights-weighted distribution. Secondly, we address the analytical
computation of weights such that the targeted frequencies are achieved
asymptotically, i. e. for large values of . We derive systems of functional
equations whose resolution gives an explicit relationship between \Weights
and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in
\bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies
associated with a given -tuple \Weights of weights, and an optimized
version in \bigO{k n^2} in the case of context-free languages. This allows
for a heuristic resolution of the weights/frequencies relationship suitable for
complex specifications. In the second alternative, the targeted distribution is
given by a natural numbers such that
where is the number of undistinguished atoms.
The structures must be generated uniformly among the set of structures of size
that contain {\em exactly} atoms \At_i (). We give
a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating
structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for
regular specifications
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