Precise n-gram Probabilities from Stochastic Context-free Grammars

We present an algorithm for computing n-gram probabilities from stochastic context-free grammars, a procedure that can alleviate some of the standard problems associated with n-grams (estimation from sparse data, lack of linguistic structure, among others). The method operates via the computation of substring expectations, which in turn is accomplished by solving systems of linear equations derived from the grammar. We discuss efficient implementation of the algorithm and report our practical experience with it.Comment: 12 pages, to appear in ACL-9

A specification language for Lexical Functional Grammars

This paper defines a language L for specifying LFG grammars. This enables constraints on LFG's composite ontology (c-structures synchronised with f-structures) to be stated directly; no appeal to the LFG construction algorithm is needed. We use L to specify schemata annotated rules and the LFG uniqueness, completeness and coherence principles. Broader issues raised by this work are noted and discussed.Comment: 6 pages, LaTeX uses eaclap.sty; Procs of Euro ACL-9

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 $n$ and a targeted distribution in $k$ of its \emph{distinguished} atoms. We consider two variations on this problem. In the first alternative, the targeted distribution is given by $k$ real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 < \TargFreq_i < 1 for all $i$ and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We aim to generate random structures among the whole set of structures of a given size $n$, 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 $k$-tuple \Weights of real-valued weights, inducing a weighted distribution over the set of structures of size $n$. 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 $m$ 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 $n$. 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 $k$-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 $k$ natural numbers $n_1, \ldots, n_k$ such that $n_1+\cdots+n_k+r=n$ where $r \geq 0$ is the number of undistinguished atoms. The structures must be generated uniformly among the set of structures of size $n$ that contain {\em exactly} $n_i$ atoms \At_i ($1 \leq i \leq k$). We give a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating $m$ structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for regular specifications

Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory

Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a Lie algebra, whose structure is reminiscent of the insertion Lie algebras of quantum field theory. We also show that the Feynman graphs of quantum field theories are graph languages generated by a theory dependent graph grammar.Comment: 19 pages, LaTeX, 3 jpeg figure

Computation of distances for regular and context-free probabilistic languages

Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe

Polynomial Time Algorithms for Multi-Type Branching Processes and Stochastic Context-Free Grammars

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where \epsilon > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open problems regarding the computational complexity of computing key quantities associated with some classic and heavily studied stochastic processes, including multi-type branching processes and stochastic context-free grammars

Equational reasoning with context-free families of string diagrams

String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we define a class of context-free grammars, called B-ESG grammars, that are suitable for defining entire families of string graphs, and crucially, of string graph rewrite rules. We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG rewrite patterns. We also show that it is possible to reason at the level of grammars by providing a simple method for transforming a grammar by string graph rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21145-9_

Automatic acquisition of Spanish LFG resources from the Cast3LB treebank

In this paper, we describe the automatic annotation of the Cast3LB Treebank with LFG f-structures for the subsequent extraction of Spanish probabilistic grammar and lexical resources. We adapt the approach and methodology of Cahill et al. (2004), O’Donovan et al. (2004) and elsewhere for English to Spanish and the Cast3LB treebank encoding. We report on the quality and coverage of the automatic f-structure annotation. Following the pipeline and integrated models of Cahill et al. (2004), we extract wide-coverage probabilistic LFG approximations and parse unseen Spanish text into f-structures. We also extend Bikel’s (2002) Multilingual Parse Engine to include a Spanish language module. Using the retrained Bikel parser in the pipeline model gives the best results against a manually constructed gold standard (73.20% predsonly f-score). We also extract Spanish lexical resources: 4090 semantic form types with 98 frame types. Subcategorised prepositions and particles are included in the frames