Regular Languages meet Prefix Sorting

Indexing strings via prefix (or suffix) sorting is, arguably, one of the most successful algorithmic techniques developed in the last decades. Can indexing be extended to languages? The main contribution of this paper is to initiate the study of the sub-class of regular languages accepted by an automaton whose states can be prefix-sorted. Starting from the recent notion of Wheeler graph [Gagie et al., TCS 2017]-which extends naturally the concept of prefix sorting to labeled graphs-we investigate the properties of Wheeler languages, that is, regular languages admitting an accepting Wheeler finite automaton. Interestingly, we characterize this family as the natural extension of regular languages endowed with the co-lexicographic ordering: when sorted, the strings belonging to a Wheeler language are partitioned into a finite number of co-lexicographic intervals, each formed by elements from a single Myhill-Nerode equivalence class. Moreover: (i) We show that every Wheeler NFA (WNFA) with $n$ states admits an equivalent Wheeler DFA (WDFA) with at most $2n-1-|\Sigma|$ states that can be computed in $O(n^3)$ time. This is in sharp contrast with general NFAs. (ii) We describe a quadratic algorithm to prefix-sort a proper superset of the WDFAs, a $O(n\log n)$-time online algorithm to sort acyclic WDFAs, and an optimal linear-time offline algorithm to sort general WDFAs. By contribution (i), our algorithms can also be used to index any WNFA at the moderate price of doubling the automaton's size. (iii) We provide a minimization theorem that characterizes the smallest WDFA recognizing the same language of any input WDFA. The corresponding constructive algorithm runs in optimal linear time in the acyclic case, and in $O(n\log n)$ time in the general case. (iv) We show how to compute the smallest WDFA equivalent to any acyclic DFA in nearly-optimal time.Comment: added minimization theorems; uploaded submitted version; New version with new results (W-MH theorem, linear determinization), added author: Giovanna D'Agostin

A Formal Framework for Linguistic Annotation

`Linguistic annotation' covers any descriptive or analytic notations applied to raw language data. The basic data may be in the form of time functions -- audio, video and/or physiological recordings -- or it may be textual. The added notations may include transcriptions of all sorts (from phonetic features to discourse structures), part-of-speech and sense tagging, syntactic analysis, `named entity' identification, co-reference annotation, and so on. While there are several ongoing efforts to provide formats and tools for such annotations and to publish annotated linguistic databases, the lack of widely accepted standards is becoming a critical problem. Proposed standards, to the extent they exist, have focussed on file formats. This paper focuses instead on the logical structure of linguistic annotations. We survey a wide variety of existing annotation formats and demonstrate a common conceptual core, the annotation graph. This provides a formal framework for constructing, maintaining and searching linguistic annotations, while remaining consistent with many alternative data structures and file formats.Comment: 49 page

Joining Extractions of Regular Expressions

Regular expressions with capture variables, also known as "regex formulas," extract relations of spans (interval positions) from text. These relations can be further manipulated via Relational Algebra as studied in the context of document spanners, Fagin et al.'s formal framework for information extraction. We investigate the complexity of querying text by Conjunctive Queries (CQs) and Unions of CQs (UCQs) on top of regex formulas. We show that the lower bounds (NP-completeness and W[1]-hardness) from the relational world also hold in our setting; in particular, hardness hits already single-character text! Yet, the upper bounds from the relational world do not carry over. Unlike the relational world, acyclic CQs, and even gamma-acyclic CQs, are hard to compute. The source of hardness is that it may be intractable to instantiate the relation defined by a regex formula, simply because it has an exponential number of tuples. Yet, we are able to establish general upper bounds. In particular, UCQs can be evaluated with polynomial delay, provided that every CQ has a bounded number of atoms (while unions and projection can be arbitrary). Furthermore, UCQ evaluation is solvable with FPT (Fixed-Parameter Tractable) delay when the parameter is the size of the UCQ

A Compact Index for Cartesian Tree Matching

Cartesian tree matching is a recently introduced string matching problem in which two strings match if their corresponding Cartesian trees are the same. It is considered appropriate to find patterns regarding their shapes especially in numerical time series data. While many related problems have been addressed, developing a compact index has received relatively less attention. In this paper, we present a 3n+o(n)-bit index that can count the number of occurrences of a Cartesian tree pattern in ?(m) time where n and m are the text and pattern length. To the best of our knowledge, this work is the first ?(n)-bit compact data structure for indexing for this problem

Automata-based Model Counting String Constraint Solver for Vulnerability Analysis

Most common vulnerabilities in modern software applications are due to errors in string manipulation code. String constraint solvers are essential components of program analysis techniques for detecting and repairing vulnerabilities that are due to string manipulation errors. In this dissertation, we present an automata-based string constraint solver for vulnerability analysis of string manipulating programs.Given a string constraint, we generate an automaton that accepts all solutions that satisfy the constraint. Our string constraint solver can also map linear arithmetic constraints to automata in order to handle constraints on string lengths. By integrating our string constraint solver to a symbolic execution tool, we can check for string manipulation errors in programs. Recently, quantitative and probabilistic program analyses techniques have been proposed which require counting the number of solutions to string constraints. We extend our string constraint solver with model counting capability based on the observation that, using an automata-based constraint representation, model counting reduces to path counting, which can be solved precisely. Our approach is parameterized in the sense that, we do notassume a finite domain size during automata construction, resulting in a potentially infinite set of solutions, and our model counting approach works for arbitrarily large bounds.We have implemented our approach in a tool called ABC (Automata-Based model Counter) using a constraint language that is compatible with the SMTLIB language specification used by satifiabilty-modula-theories solvers. This SMTLIB interface facilitates integration of our constraint solver with existing symbolic execution tools. We demonstrate the effectiveness of ABC on a large set of string constraints extracted from real-world web applications.We also present automata-based testing techniques for string manipulating programs. A vulnerability signature is a characterization of all user inputs that can be used to exploit a vulnerability. Automata-based static string analysis techniques allow automated computation of vulnerability signatures represented as automata. Given a vulnerability signature represented as an automaton, we present algorithms for test case generation based on state, transition, and path coverage. These automaticallygenerated test cases can be used to test applications that are not analyzable statically, and to discover attack strings that demonstrate how the vulnerabilities can be exploited. We experimentally comparedifferent coverage criteria and demonstrate the effectiveness of our test generation approach

Three Essays on Enhancing Clinical Trial Subject Recruitment Using Natural Language Processing and Text Mining

Patient recruitment and enrollment are critical factors for a successful clinical trial; however, recruitment tends to be the most common problem in most clinical trials. The success of a clinical trial depends on efficiently recruiting suitable patients to conduct the trial. Every clinical trial research has a protocol, which describes what will be done in the study and how it will be conducted. Also, the protocol ensures the safety of the trial subjects and the integrity of the data collected. The eligibility criteria section of clinical trial protocols is important because it specifies the necessary conditions that participants have to satisfy. Since clinical trial eligibility criteria are usually written in free text form, they are not computer interpretable. To automate the analysis of the eligibility criteria, it is therefore necessary to transform those criteria into a computer-interpretable format. Unstructured format of eligibility criteria additionally create search efficiency issues. Thus, searching and selecting appropriate clinical trials for a patient from relatively large number of available trials is a complex task. A few attempts have been made to automate the matching process between patients and clinical trials. However, those attempts have not fully integrated the entire matching process and have not exploited the state-of-the-art Natural Language Processing (NLP) techniques that may improve the matching performance. Given the importance of patient recruitment in clinical trial research, the objective of this research is to automate the matching process using NLP and text mining techniques and, thereby, improve the efficiency and effectiveness of the recruitment process. This dissertation research, which comprises three essays, investigates the issues of clinical trial subject recruitment using state-of-the-art NLP and text mining techniques. Essay 1: Building a Domain-Specific Lexicon for Clinical Trial Subject Eligibility Analysis Essay 2: Clustering Clinical Trials Using Semantic-Based Feature Expansion Essay 3: An Automatic Matching Process of Clinical Trial Subject Recruitment In essay1, I develop a domain-specific lexicon for n-gram Named Entity Recognition (NER) in the breast cancer domain. The domain-specific dictionary is used for selection and reduction of n-gram features in clustering in eassy2. The domain-specific dictionary was evaluated by comparing it with Systematized Nomenclature of Medicine--Clinical Terms (SNOMED CT). The results showed that it add significant number of new terms which is very useful in effective natural language processing In essay 2, I explore the clustering of similar clinical trials using the domain-specific lexicon and term expansion using synonym from the Unified Medical Language System (UMLS). I generate word n-gram features and modify the features with the domain-specific dictionary matching process. In order to resolve semantic ambiguity, a semantic-based feature expansion technique using UMLS is applied. A hierarchical agglomerative clustering algorithm is used to generate clinical trial clusters. The focus is on summarization of clinical trial information in order to enhance trial search efficiency. Finally, in essay 3, I investigate an automatic matching process of clinical trial clusters and patient medical records. The patient records collected from a prior study were used to test our approach. The patient records were pre-processed by tokenization and lemmatization. The pre-processed patient information were then further enhanced by matching with breast cancer custom dictionary described in essay 1 and semantic feature expansion using UMLS Metathesaurus. Finally, I matched the patient record with clinical trial clusters to select the best matched cluster(s) and then with trials within the clusters. The matching results were evaluated by internal expert as well as external medical expert