Weighted DAG Automata for Semantic Graphs

Graphs have a variety of uses in natural language processing, particularly as representations of linguistic meaning. A deficit in this area of research is a formal framework for creating, combining, and using models involving graphs that parallels the frameworks of finite automata for strings and finite tree automata for trees. A possible starting point for such a framework is the formalism of directed acyclic graph (DAG) automata, defined by Kamimura and Slutzki and extended by Quernheim and Knight. In this article, we study the latter in depth, demonstrating several new results, including a practical recognition algorithm that can be used for inference and learning with models defined on DAG automata. We also propose an extension to graphs with unbounded node degree and show that our results carry over to the extended formalism

The problem with probabilistic DAG automata for semantic graphs

Semantic representations in the form of directed acyclic graphs (DAGs) have been introduced in recent years, and to model them, we need probabilistic models of DAGs. One model that has attracted some attention is the DAG automaton, but it has not been studied as a probabilistic model. We show that some DAG automata cannot be made into useful probabilistic models by the nearly universal strategy of assigning weights to transitions. The problem affects single-rooted, multi-rooted, and unbounded-degree variants of DAG automata, and appears to be pervasive. It does not affect planar variants, but these are problematic for other reasons.Comment: To appear in NAACL-HLT 201

Probabilistic graph formalisms for meaning representations

In recent years, many datasets have become available that represent natural language semantics as graphs. To use these datasets in natural language processing (NLP), we require probabilistic models of graphs. Finite-state models have been very successful for NLP tasks on strings and trees because they are probabilistic and composable. Are there equivalent models for graphs? In this thesis, we survey several graph formalisms, focusing on whether they are probabilistic and composable, and we contribute several new results. In particular, we study the directed acyclic graph automata languages (DAGAL), the monadic second-order graph languages (MSOGL), and the hyperedge replacement languages (HRL). We prove that DAGAL cannot be made probabilistic, we explain why MSOGL also most likely cannot be made probabilistic, and we review the fact that HRL are not composable. We then review a subfamily of HRL and MSOGL: the regular graph languages (RGL; Courcelle 1991), which have not been widely studied, and particularly have not been studied in an NLP context. Although Courcelle (1991) only sketches a proof, we present a full, more NLP-accessible proof that RGL are a subfamily of MSOGL. We prove that RGL are probabilistic and composable, and we provide a novel Earley-style parsing algorithm for them that runs in time linear in the size of the input graph. We compare RGL to two other new formalisms: the restricted DAG languages (RDL; Bj¨orklund et al. 2016) and the tree-like languages (TLL; Matheja et al. 2015). We show that RGL and RDL are incomparable; TLL and RDL are incomparable; and either RGL are incomparable to TLL, or RGL are contained within TLL. This thesis provides a clearer picture of this field from an NLP perspective, and suggests new theoretical and empirical research directions

Polyglot Semantic Parsing in APIs

Traditional approaches to semantic parsing (SP) work by training individual models for each available parallel dataset of text-meaning pairs. In this paper, we explore the idea of polyglot semantic translation, or learning semantic parsing models that are trained on multiple datasets and natural languages. In particular, we focus on translating text to code signature representations using the software component datasets of Richardson and Kuhn (2017a,b). The advantage of such models is that they can be used for parsing a wide variety of input natural languages and output programming languages, or mixed input languages, using a single unified model. To facilitate modeling of this type, we develop a novel graph-based decoding framework that achieves state-of-the-art performance on the above datasets, and apply this method to two other benchmark SP tasks.Comment: accepted for NAACL-2018 (camera ready version

Semantic Graph Parsing with Recurrent Neural Network DAG Grammars

Semantic parses are directed acyclic graphs (DAGs), so semantic parsing should be modeled as graph prediction. But predicting graphs presents difficult technical challenges, so it is simpler and more common to predict the linearized graphs found in semantic parsing datasets using well-understood sequence models. The cost of this simplicity is that the predicted strings may not be well-formed graphs. We present recurrent neural network DAG grammars, a graph-aware sequence model that ensures only well-formed graphs while sidestepping many difficulties in graph prediction. We test our model on the Parallel Meaning Bank---a multilingual semantic graphbank. Our approach yields competitive results in English and establishes the first results for German, Italian and Dutch.Comment: 9 pages, to appear in EMNLP201

Survey on Instruction Selection: An Extensive and Modern Literature Review

Instruction selection is one of three optimisation problems involved in the code generator backend of a compiler. The instruction selector is responsible of transforming an input program from its target-independent representation into a target-specific form by making best use of the available machine instructions. Hence instruction selection is a crucial part of efficient code generation. Despite on-going research since the late 1960s, the last, comprehensive survey on the field was written more than 30 years ago. As new approaches and techniques have appeared since its publication, this brings forth a need for a new, up-to-date review of the current body of literature. This report addresses that need by performing an extensive review and categorisation of existing research. The report therefore supersedes and extends the previous surveys, and also attempts to identify where future research should be directed.Comment: Major changes: - Merged simulation chapter with macro expansion chapter - Addressed misunderstandings of several approaches - Completely rewrote many parts of the chapters; strengthened the discussion of many approaches - Revised the drawing of all trees and graphs to put the root at the top instead of at the bottom - Added appendix for listing the approaches in a table See doc for more inf

A Trichotomy for Regular Simple Path Queries on Graphs

Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes. Those regular simple path queries (RSPQs) find several applications in practice, yet they quickly become intractable, even for basic languages such as (aa)* or a*ba*. In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem. More precisely, we identify the fragment that is maximal in the following sense: regular simple path queries can be evaluated in polynomial time for every regular language L that belongs to this fragment and evaluation is NP-complete for languages outside this fragment. We thus fully characterize the frontier between tractability and intractability for RSPQs, and we refine our results to show the following trichotomy: Evaluations of RSPQs is either AC0, NL-complete or NP-complete in data complexity, depending on the regular language L. The fragment identified also admits a simple characterization in terms of regular expressions. Finally, we also discuss the complexity of the following decision problem: decide, given a language L, whether finding a regular simple path for L is tractable. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is NL-complete for the first representation and PSPACE-complete for the other two. As a conclusion we extend our results from edge-labeled graphs to vertex-labeled graphs and vertex-edge labeled graphs.Comment: 15 pages, conference submissio