Assumptions behind grammatical approaches to code-switching: when the blueprint is a red herring

Many of the so-called ‘grammars’ of code-switching are based on various underlying assumptions, e.g. that informal speech can be adequately or appropriately described in terms of ‘‘grammar’’; that deep, rather than surface, structures are involved in code-switching; that one ‘language’ is the ‘base’ or ‘matrix’; and that constraints derived from existing data are universal and predictive. We question these assumptions on several grounds. First, ‘grammar’ is arguably distinct from the processes driving speech production. Second, the role of grammar is mediated by the variable, poly-idiolectal repertoires of bilingual speakers. Third, in many instances of CS the notion of a ‘base’ system is either irrelevant, or fails to explain the facts. Fourth, sociolinguistic factors frequently override ‘grammatical’ factors, as evidence from the same language pairs in different settings has shown. No principles proposed to date account for all the facts, and it seems unlikely that ‘grammar’, as conventionally conceived, can provide definitive answers. We conclude that rather than seeking universal, predictive grammatical rules, research on CS should focus on the variability of bilingual grammars

If the Current Clique Algorithms are Optimal, so is Valiant's Parser

The CFG recognition problem is: given a context-free grammar $\mathcal{G}$ and a string $w$ of length $n$, decide if $w$ can be obtained from $\mathcal{G}$. This is the most basic parsing question and is a core computer science problem. Valiant's parser from 1975 solves the problem in $O(n^{\omega})$ time, where $\omega<2.373$ 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 $O(n^3/\log^3{n})$ 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 $O(|\mathcal{G}|\cdot n^{3-\varepsilon})$ can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication. Unfortunately, Lee's hardness result required that the grammar size be $|\mathcal{G}|=\Omega(n^6)$. 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 $k$-Clique problem: given a graph on $n$ nodes, decide if there are $k$ 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)

Rule-restricted Automaton-grammar transducers: Power and Linguistic Applications

This paper introduces the notion of a new transducer as a two-component system, which consists of a nite automaton and a context-free grammar. In essence, while the automaton reads its input string, the grammar produces its output string, and their cooperation is controlled by a set, which restricts the usage of their rules. From a theoretical viewpoint, the present paper discusses the power of this system working in an ordinary way as well as in a leftmost way. In addition, the paper introduces an appearance checking, which allows us to check whether some symbols are present in the rewritten string, and studies its e ect on the power. It achieves the following three main results. First, the system generates and accepts languages de ned by matrix grammars and partially blind multi-counter automata, respectively. Second, if we place a leftmost restriction on derivation in the context-free grammar, both accepting and generating power of the system is equal to generative power of context-free grammars. Third, the system with appearance checking can accept and generate all recursively enumerable languages. From more pragmatical viewpoint, this paper describes several linguistic applications. A special attention is paid to the Japanese-Czech translation

Syntactic Analysis Based on Matrix Grammar

Tato bakalářská práce se zabývá syntaktickou analýzou založenou na maticových gramatikách. V teoretické části nejdříve přináší několik různých pohledů na tento typ řízených gramatik a zkoumá podobnosti s klasickými bezkontextovými gramatikami. Z těchto podobností se poté v praktické části snaží vycházet při návrhu modelu prediktivní syntaktické analýzy pro některé kontextové jazyky, ke kterým můžeme sestrojit odpovídající maticové gramatiky, které je generují. V práci jsou rovněž prezentovány některé experimentální algoritmy a návrh řešení, které by se daly spíše využít při dalším vývoji projektu.The subject of this thesis is to develop a method of syntactic analysis based on matrix grammar s. In its theoretical part we provide various analytical aspects for this type of regulated grammar in order to reveal the common background as well as search for similarities with the classical context-free grammars which we will then be able to benefit from in the practical part. Our goal is to extend the well-known predictive method of syntactic analysis to further accept a wider spectrum of formal languages - some of the context-sensitive ones which we are able to generate using our matrix grammars. Besides this main effort we also present some experimental algorithms and suggestions hich could be used in further research of this project.

Labeling Workflow Views with Fine-Grained Dependencies

This paper considers the problem of efficiently answering reachability queries over views of provenance graphs, derived from executions of workflows that may include recursion. Such views include composite modules and model fine-grained dependencies between module inputs and outputs. A novel view-adaptive dynamic labeling scheme is developed for efficient query evaluation, in which view specifications are labeled statically (i.e. as they are created) and data items are labeled dynamically as they are produced during a workflow execution. Although the combination of fine-grained dependencies and recursive workflows entail, in general, long (linear-size) data labels, we show that for a large natural class of workflows and views, labels are compact (logarithmic-size) and reachability queries can be evaluated in constant time. Experimental results demonstrate the benefit of this approach over the state-of-the-art technique when applied for labeling multiple views.Comment: VLDB201

Parsing with CYK over Distributed Representations

Syntactic parsing is a key task in natural language processing. This task has been dominated by symbolic, grammar-based parsers. Neural networks, with their distributed representations, are challenging these methods. In this article we show that existing symbolic parsing algorithms can cross the border and be entirely formulated over distributed representations. To this end we introduce a version of the traditional Cocke-Younger-Kasami (CYK) algorithm, called D-CYK, which is entirely defined over distributed representations. Our D-CYK uses matrix multiplication on real number matrices of size independent of the length of the input string. These operations are compatible with traditional neural networks. Experiments show that our D-CYK approximates the original CYK algorithm. By showing that CYK can be entirely performed on distributed representations, we open the way to the definition of recurrent layers of CYK-informed neural networks.Comment: The algorithm has been greatly improved. Experiments have been redesigne

Weakly Restricted Stochastic Grammars

A new type of stochastic grammars is introduced for investigation: weakly restricted stochastic grammars. In this paper we will concentrate on the consistency problem. To find conditions for stochastic grammars to be consistent, the theory of multitype Galton-Watson branching processes and generating functions is of central importance.\ud The unrestricted stochastic grammar formalism generates the same class of languages as the weakly restricted formalism. The inside-outside algorithm is adapted for use with weakly restricted grammars