412 research outputs found
A Transition-Based Directed Acyclic Graph Parser for UCCA
We present the first parser for UCCA, a cross-linguistically applicable
framework for semantic representation, which builds on extensive typological
work and supports rapid annotation. UCCA poses a challenge for existing parsing
techniques, as it exhibits reentrancy (resulting in DAG structures),
discontinuous structures and non-terminal nodes corresponding to complex
semantic units. To our knowledge, the conjunction of these formal properties is
not supported by any existing parser. Our transition-based parser, which uses a
novel transition set and features based on bidirectional LSTMs, has value not
just for UCCA parsing: its ability to handle more general graph structures can
inform the development of parsers for other semantic DAG structures, and in
languages that frequently use discontinuous structures.Comment: 16 pages; Accepted as long paper at ACL201
Tabular Parsing
This is a tutorial on tabular parsing, on the basis of tabulation of
nondeterministic push-down automata. Discussed are Earley's algorithm, the
Cocke-Kasami-Younger algorithm, tabular LR parsing, the construction of parse
trees, and further issues.Comment: 21 pages, 14 figure
Left Recursion in Parsing Expression Grammars
Parsing Expression Grammars (PEGs) are a formalism that can describe all
deterministic context-free languages through a set of rules that specify a
top-down parser for some language. PEGs are easy to use, and there are
efficient implementations of PEG libraries in several programming languages.
A frequently missed feature of PEGs is left recursion, which is commonly used
in Context-Free Grammars (CFGs) to encode left-associative operations. We
present a simple conservative extension to the semantics of PEGs that gives
useful meaning to direct and indirect left-recursive rules, and show that our
extensions make it easy to express left-recursive idioms from CFGs in PEGs,
with similar results. We prove the conservativeness of these extensions, and
also prove that they work with any left-recursive PEG.
PEGs can also be compiled to programs in a low-level parsing machine. We
present an extension to the semantics of the operations of this parsing machine
that let it interpret left-recursive PEGs, and prove that this extension is
correct with regards to our semantics for left-recursive PEGs.Comment: Extended version of the paper "Left Recursion in Parsing Expression
Grammars", that was published on 2012 Brazilian Symposium on Programming
Language
Probabilistic Parsing Strategies
We present new results on the relation between purely symbolic context-free
parsing strategies and their probabilistic counter-parts. Such parsing
strategies are seen as constructions of push-down devices from grammars. We
show that preservation of probability distribution is possible under two
conditions, viz. the correct-prefix property and the property of strong
predictiveness. These results generalize existing results in the literature
that were obtained by considering parsing strategies in isolation. From our
general results we also derive negative results on so-called generalized LR
parsing.Comment: 36 pages, 1 figur
If the Current Clique Algorithms are Optimal, so is Valiant's Parser
The CFG recognition problem is: given a context-free grammar
and a string of length , decide if can be obtained from
. This is the most basic parsing question and is a core computer
science problem. Valiant's parser from 1975 solves the problem in
time, where is the matrix multiplication
exponent. Dozens of parsing algorithms have been proposed over the years, yet
Valiant's upper bound remains unbeaten. The best combinatorial algorithms have
mildly subcubic complexity.
Lee (JACM'01) provided evidence that fast matrix multiplication is needed for
CFG parsing, and that very efficient and practical algorithms might be hard or
even impossible to obtain. Lee showed that any algorithm for a more general
parsing problem with running time can
be converted into a surprising subcubic algorithm for Boolean Matrix
Multiplication. Unfortunately, Lee's hardness result required that the grammar
size be . Nothing was known for the more relevant
case of constant size grammars.
In this work, we prove that any improvement on Valiant's algorithm, even for
constant size grammars, either in terms of runtime or by avoiding the
inefficiencies of fast matrix multiplication, would imply a breakthrough
algorithm for the -Clique problem: given a graph on nodes, decide if
there are that form a clique.
Besides classifying the complexity of a fundamental problem, our reduction
has led us to similar lower bounds for more modern and well-studied cubic time
problems for which faster algorithms are highly desirable in practice: RNA
Folding, a central problem in computational biology, and Dyck Language Edit
Distance, answering an open question of Saha (FOCS'14)
Certified Context-Free Parsing: A formalisation of Valiant's Algorithm in Agda
Valiant (1975) has developed an algorithm for recognition of context free
languages. As of today, it remains the algorithm with the best asymptotic
complexity for this purpose. In this paper, we present an algebraic
specification, implementation, and proof of correctness of a generalisation of
Valiant's algorithm. The generalisation can be used for recognition, parsing or
generic calculation of the transitive closure of upper triangular matrices. The
proof is certified by the Agda proof assistant. The certification is
representative of state-of-the-art methods for specification and proofs in
proof assistants based on type-theory. As such, this paper can be read as a
tutorial for the Agda system
An Efficient Probabilistic Context-Free Parsing Algorithm that Computes Prefix Probabilities
We describe an extension of Earley's parser for stochastic context-free
grammars that computes the following quantities given a stochastic context-free
grammar and an input string: a) probabilities of successive prefixes being
generated by the grammar; b) probabilities of substrings being generated by the
nonterminals, including the entire string being generated by the grammar; c)
most likely (Viterbi) parse of the string; d) posterior expected number of
applications of each grammar production, as required for reestimating rule
probabilities. (a) and (b) are computed incrementally in a single left-to-right
pass over the input. Our algorithm compares favorably to standard bottom-up
parsing methods for SCFGs in that it works efficiently on sparse grammars by
making use of Earley's top-down control structure. It can process any
context-free rule format without conversion to some normal form, and combines
computations for (a) through (d) in a single algorithm. Finally, the algorithm
has simple extensions for processing partially bracketed inputs, and for
finding partial parses and their likelihoods on ungrammatical inputs.Comment: 45 pages. Slightly shortened version to appear in Computational
Linguistics 2
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
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