Cluster Editing Parameterized Above Modification-Disjoint P?-Packings

Given a graph G = (V,E) and an integer k, the Cluster Editing problem asks whether we can transform G into a union of vertex-disjoint cliques by at most k modifications (edge deletions or insertions). In this paper, we study the following variant of Cluster Editing. We are given a graph G = (V,E), a packing ? of modification-disjoint induced P?s (no pair of P?s in H share an edge or non-edge) and an integer ?. The task is to decide whether G can be transformed into a union of vertex-disjoint cliques by at most ?+|H| modifications (edge deletions or insertions). We show that this problem is NP-hard even when ? = 0 (in which case the problem asks to turn G into a disjoint union of cliques by performing exactly one edge deletion or insertion per element of H) and when each vertex is in at most 23 P?s of the packing. This answers negatively a question of van Bevern, Froese, and Komusiewicz (CSR 2016, ToCS 2018), repeated by C. Komusiewicz at Shonan meeting no. 144 in March 2019. We then initiate the study to find the largest integer c such that the problem remains tractable when restricting to packings such that each vertex is in at most c packed P?s. Van Bevern et al. showed that the case c = 1 is fixed-parameter tractable with respect to ? and we show that the case c = 2 is solvable in |V|^{2? + O(1)} time

Онтологія аналізу Big Data

The object of this research is the Big Data (BD) analysis processes. One of the most problematic places is the lack of a clear classification of BD analysis methods, the presence of which will greatly facilitate the selection of an optimal and efficient algorithm for analyzing these data depending on their structure.In the course of the study, Data Mining methods, Technologies Tech Mining, MapReduce technology, data visualization, other technologies and analysis techniques were used. This allows to determine their main characteristics and features for constructing a formal analysis model for Big Data. The rules for analyzing Big Data in the form of an ontological knowledge base are developed with the aim of using it to process and analyze any data.A classifier for forming a set of Big Data analysis rules has been obtained. Each BD has a set of parameters and criteria that determine the methods and technologies of analysis. The very purpose of BD, its structure and content determine the techniques and technologies for further analysis. Thanks to the developed ontology of the knowledge base of BD analysis with Protégé 3.4.7 and the set of RABD rules built in them, the process of selecting the methodologies and technologies for further analysis is shortened and the analysis of the selected BD is automated. This is due to the fact that the proposed approach to the analysis of Big Data has a number of features, in particular ontological knowledge base based on modern methods of artificial intelligence.Thanks to this, it is possible to obtain a complete set of Big Data analysis rules. This is possible only if the parameters and criteria of a specific Big Data are analyzed clearly.Исследованы процессы анализа Big Data. Используя разработанную формальную модель и проведенный критический анализ методов и технологий анализа Big Data, построена онтология анализа Big Data. Исследованы методы, модели и инструменты для усовершенствования онтологии аналитики Big Data и эффективной поддержки разработки структурных элементов модели системы поддержки принятия решений по управлению Big Data.Досліджені процеси аналізу Big Data. Використовуючи розроблену формальну модель та проведений критичний аналіз методів і технологій аналізу Big Data, побудовано онтологію аналізу Big Data. Досліджено методи, моделі та інструменти для удосконалення онтології аналітики Big Data та ефективнішої підтримки розроблення структурних елементів моделі системи підтримки прийняття рішень з керування Big Data

Онтологія аналізу Big Data

The object of this research is the Big Data (BD) analysis processes. One of the most problematic places is the lack of a clear classification of BD analysis methods, the presence of which will greatly facilitate the selection of an optimal and efficient algorithm for analyzing these data depending on their structure.In the course of the study, Data Mining methods, Technologies Tech Mining, MapReduce technology, data visualization, other technologies and analysis techniques were used. This allows to determine their main characteristics and features for constructing a formal analysis model for Big Data. The rules for analyzing Big Data in the form of an ontological knowledge base are developed with the aim of using it to process and analyze any data.A classifier for forming a set of Big Data analysis rules has been obtained. Each BD has a set of parameters and criteria that determine the methods and technologies of analysis. The very purpose of BD, its structure and content determine the techniques and technologies for further analysis. Thanks to the developed ontology of the knowledge base of BD analysis with Protégé 3.4.7 and the set of RABD rules built in them, the process of selecting the methodologies and technologies for further analysis is shortened and the analysis of the selected BD is automated. This is due to the fact that the proposed approach to the analysis of Big Data has a number of features, in particular ontological knowledge base based on modern methods of artificial intelligence.Thanks to this, it is possible to obtain a complete set of Big Data analysis rules. This is possible only if the parameters and criteria of a specific Big Data are analyzed clearly.Исследованы процессы анализа Big Data. Используя разработанную формальную модель и проведенный критический анализ методов и технологий анализа Big Data, построена онтология анализа Big Data. Исследованы методы, модели и инструменты для усовершенствования онтологии аналитики Big Data и эффективной поддержки разработки структурных элементов модели системы поддержки принятия решений по управлению Big Data.Досліджені процеси аналізу Big Data. Використовуючи розроблену формальну модель та проведений критичний аналіз методів і технологій аналізу Big Data, побудовано онтологію аналізу Big Data. Досліджено методи, моделі та інструменти для удосконалення онтології аналітики Big Data та ефективнішої підтримки розроблення структурних елементів моделі системи підтримки прийняття рішень з керування Big Data

Guidance in the human–machine analytics process

In this paper, we list the goals for and the pros and cons of guidance, and we discuss the role that it can play not only in key low-level visualization tasks but also the more sophisticated model-generation tasks of visual analytics. Recent advances in artificial intelligence, particularly in machine learning, have led to high hopes regarding the possibilities of using automatic techniques to perform some of the tasks that are currently done manually using visualization by data analysts. However, visual analytics remains a complex activity, combining many different subtasks. Some of these tasks are relatively low-level, and it is clear how automation could play a role—for example, classification and clustering of data. Other tasks are much more abstract and require significant human creativity, for example, linking insights gleaned from a variety of disparate and heterogeneous data artifacts to build support for decision making. In this paper, we outline the potential applications of guidance, as well as the inputs to guidance. We discuss challenges in implementing guidance, including the inputs to guidance systems and how to provide guidance to users. We propose potential methods for evaluating the quality of guidance at different phases in the analytic process and introduce the potential negative effects of guidance as a source of bias in analytic decision making

セキュアRFIDタグチップの設計論

In this thesis, we focus on radio frequency identification (RFID) tag. We design, implement, and evaluate hardware performance of a secure tag that runs the authentication protocol based on cryptographic algorithms. The cryptographic algorithm and the pseudorandom number generator are required to be implemented in the tag. To realize the secure tag, we tackle the following four steps: (A) decision of hardware architecture for the authentication protocol, (B) selection of the cryptographic algorithm, (C) establishment of a pseudorandom number generating method, and (D) implementation and performance evaluation of a silicon chip on an RFID system.(A) The cryptographic algorithm and the pseudorandom number generator are repeatedly called for each authentication. Therefore, the impact of the time needed for the cryptographic processes on the hardware performance of the tag can be large. While low-area requirements have been mainly discussed in the previous studies, it is needed to discuss the hardware architecture for the authentication protocol from the viewpoint of the operating time. In this thesis, in order to decide the hardware architecture, we evaluate hardware performance in the sense of the operating time. As a result, the parallel architecture is suitable for hash functions that are widely used for tag authentication protocols.(B) A lot of cryptographic algorithms have been developed and hardware performance of the algorithms have been evaluated on different conditions. However, as the evaluation results depend on the conditions, it is hard to compare the previous results. In addition, the interface of the cryptographic circuits has not been paid attention. In this thesis, in order to select a cryptographic algorithm, we design the interface of the cryptographic circuits to meet with the tag, and evaluate hardware performance of the circuits on the same condition. As a result, the lightweight hash function SPONGENT-160 achieves well-balanced hardware performance.(C) Implementation of a pseudorandom number generator based on the performance evaluation results on (B) can be a method to generate pseudorandom number on the tag. On the other hand, as the cryptographic algorithm and the pseudorandom number generator are not used simultaneously on the authentication protocol. Therefore, if the cryptographic circuit could be used for pseudorandom number generation, the hardware resource on the tag can be exploited efficiently. In this thesis, we propose a pseudorandom number generating method using a hash function that is a cryptographic component of the authentication protocol. Through the evaluation of our proposed method, we establish a lightweight pseudorandom number generating method for the tag.(D) Tag authentication protocols using a cryptographic algorithm have been developed in the previous studies. However, hardware implementation and performance evaluation of a tag, which runs authentication processes, have not been studied. In this thesis, we design and do a single chip implementation of an analog front-end block and a digital processing block including the results on (A), (B), and (C). Then, we evaluate hardware performance of the tag. As a result, we show that a tag, which runs the authentication protocol based on cryptographic algorithms, is feasible.電気通信大学201

Real-time generation and adaptation of social companion robot behaviors

Social robots will be part of our future homes. They will assist us in everyday tasks, entertain us, and provide helpful advice. However, the technology still faces challenges that must be overcome to equip the machine with social competencies and make it a socially intelligent and accepted housemate. An essential skill of every social robot is verbal and non-verbal communication. In contrast to voice assistants, smartphones, and smart home technology, which are already part of many people's lives today, social robots have an embodiment that raises expectations towards the machine. Their anthropomorphic or zoomorphic appearance suggests they can communicate naturally with speech, gestures, or facial expressions and understand corresponding human behaviors. In addition, robots also need to consider individual users' preferences: everybody is shaped by their culture, social norms, and life experiences, resulting in different expectations towards communication with a robot. However, robots do not have human intuition - they must be equipped with the corresponding algorithmic solutions to these problems. This thesis investigates the use of reinforcement learning to adapt the robot's verbal and non-verbal communication to the user's needs and preferences. Such non-functional adaptation of the robot's behaviors primarily aims to improve the user experience and the robot's perceived social intelligence. The literature has not yet provided a holistic view of the overall challenge: real-time adaptation requires control over the robot's multimodal behavior generation, an understanding of human feedback, and an algorithmic basis for machine learning. Thus, this thesis develops a conceptual framework for designing real-time non-functional social robot behavior adaptation with reinforcement learning. It provides a higher-level view from the system designer's perspective and guidance from the start to the end. It illustrates the process of modeling, simulating, and evaluating such adaptation processes. Specifically, it guides the integration of human feedback and social signals to equip the machine with social awareness. The conceptual framework is put into practice for several use cases, resulting in technical proofs of concept and research prototypes. They are evaluated in the lab and in in-situ studies. These approaches address typical activities in domestic environments, focussing on the robot's expression of personality, persona, politeness, and humor. Within this scope, the robot adapts its spoken utterances, prosody, and animations based on human explicit or implicit feedback.Soziale Roboter werden Teil unseres zukünftigen Zuhauses sein. Sie werden uns bei alltäglichen Aufgaben unterstützen, uns unterhalten und uns mit hilfreichen Ratschlägen versorgen. Noch gibt es allerdings technische Herausforderungen, die zunächst überwunden werden müssen, um die Maschine mit sozialen Kompetenzen auszustatten und zu einem sozial intelligenten und akzeptierten Mitbewohner zu machen. Eine wesentliche Fähigkeit eines jeden sozialen Roboters ist die verbale und nonverbale Kommunikation. Im Gegensatz zu Sprachassistenten, Smartphones und Smart-Home-Technologien, die bereits heute Teil des Lebens vieler Menschen sind, haben soziale Roboter eine Verkörperung, die Erwartungen an die Maschine weckt. Ihr anthropomorphes oder zoomorphes Aussehen legt nahe, dass sie in der Lage sind, auf natürliche Weise mit Sprache, Gestik oder Mimik zu kommunizieren, aber auch entsprechende menschliche Kommunikation zu verstehen. Darüber hinaus müssen Roboter auch die individuellen Vorlieben der Benutzer berücksichtigen. So ist jeder Mensch von seiner Kultur, sozialen Normen und eigenen Lebenserfahrungen geprägt, was zu unterschiedlichen Erwartungen an die Kommunikation mit einem Roboter führt. Roboter haben jedoch keine menschliche Intuition - sie müssen mit entsprechenden Algorithmen für diese Probleme ausgestattet werden. In dieser Arbeit wird der Einsatz von bestärkendem Lernen untersucht, um die verbale und nonverbale Kommunikation des Roboters an die Bedürfnisse und Vorlieben des Benutzers anzupassen. Eine solche nicht-funktionale Anpassung des Roboterverhaltens zielt in erster Linie darauf ab, das Benutzererlebnis und die wahrgenommene soziale Intelligenz des Roboters zu verbessern. Die Literatur bietet bisher keine ganzheitliche Sicht auf diese Herausforderung: Echtzeitanpassung erfordert die Kontrolle über die multimodale Verhaltenserzeugung des Roboters, ein Verständnis des menschlichen Feedbacks und eine algorithmische Basis für maschinelles Lernen. Daher wird in dieser Arbeit ein konzeptioneller Rahmen für die Gestaltung von nicht-funktionaler Anpassung der Kommunikation sozialer Roboter mit bestärkendem Lernen entwickelt. Er bietet eine übergeordnete Sichtweise aus der Perspektive des Systemdesigners und eine Anleitung vom Anfang bis zum Ende. Er veranschaulicht den Prozess der Modellierung, Simulation und Evaluierung solcher Anpassungsprozesse. Insbesondere wird auf die Integration von menschlichem Feedback und sozialen Signalen eingegangen, um die Maschine mit sozialem Bewusstsein auszustatten. Der konzeptionelle Rahmen wird für mehrere Anwendungsfälle in die Praxis umgesetzt, was zu technischen Konzeptnachweisen und Forschungsprototypen führt, die in Labor- und In-situ-Studien evaluiert werden. Diese Ansätze befassen sich mit typischen Aktivitäten in häuslichen Umgebungen, wobei der Schwerpunkt auf dem Ausdruck der Persönlichkeit, dem Persona, der Höflichkeit und dem Humor des Roboters liegt. In diesem Rahmen passt der Roboter seine Sprache, Prosodie, und Animationen auf Basis expliziten oder impliziten menschlichen Feedbacks an

An interdisciplinary concept for human-centered explainable artificial intelligence - Investigating the impact of explainable AI on end-users

Since the 1950s, Artificial Intelligence (AI) applications have captivated people. However, this fascination has always been accompanied by disillusionment about the limitations of this technology. Today, machine learning methods such as Deep Neural Networks (DNN) are successfully used in various tasks. However, these methods also have limitations: Their complexity makes their decisions no longer comprehensible to humans - they are black-boxes. The research branch of Explainable AI (XAI) has addressed this problem by investigating how to make AI decisions comprehensible. This desire is not new. In the 1970s, developers of intrinsic explainable AI approaches, so-called white-boxes (e.g., rule-based systems), were dealing with AI explanations. Nowadays, with the increased use of AI systems in all areas of life, the design of comprehensible systems has become increasingly important. Developing such systems is part of Human-Centred AI (HCAI) research, which integrates human needs and abilities in the design of AI interfaces. For this, an understanding is needed of how humans perceive XAI and how AI explanations influence the interaction between humans and AI. One of the open questions concerns the investigation of XAI for end-users, i.e., people who have no expertise in AI but interact with such systems or are impacted by the system's decisions. This dissertation investigates the impact of different levels of interactive XAI of white- and black-box AI systems on end-users perceptions. Based on an interdisciplinary concept presented in this work, it is examined how the content, type, and interface of explanations of DNN (black box) and rule-based systems (white box) are perceived by end-users. How XAI influences end-users mental models, trust, self-efficacy, cognitive workload, and emotional state regarding the AI system is the centre of the investigation. At the beginning of the dissertation, general concepts regarding AI, explanations, and psychological constructs of mental models, trust, self-efficacy, cognitive load, and emotions are introduced. Subsequently, related work regarding the design and investigation of XAI for users is presented. This serves as a basis for the concept of a Human-Centered Explainable AI (HC-XAI) presented in this dissertation, which combines an XAI design approach with user evaluations. The author pursues an interdisciplinary approach that integrates knowledge from the research areas of (X)AI, Human-Computer Interaction, and Psychology. Based on this interdisciplinary concept, a five-step approach is derived and applied to illustrative surveys and experiments in the empirical part of this dissertation. To illustrate the first two steps, a persona approach for HC-XAI is presented, and based on that, a template for designing personas is provided. To illustrate the usage of the template, three surveys are presented that ask end-users about their attitudes and expectations towards AI and XAI. The personas generated from the survey data indicate that end-users often lack knowledge of XAI and that their perception of it depends on demographic and personality-related characteristics. Steps three to five deal with the design of XAI for concrete applications. For this, different levels of interactive XAI are presented and investigated in experiments with end-users. For this purpose, two rule-based systems (i.e., white-box) and four systems based on DNN (i.e., black-box) are used. These are applied for three purposes: Cooperation & collaboration, education, and medical decision support. Six user studies were conducted for this purpose, which differed in the interactivity of the XAI system used. The results show that end-users trust and mental models of AI depend strongly on the context of use and the design of the explanation itself. For example, explanations that a virtual agent mediates are shown to promote trust. The content and type of explanations are also perceived differently by users. The studies also show that end-users in different application contexts of XAI feel the desire for interactive explanations. The dissertation concludes with a summary of the scientific contribution, points out limitations of the presented work, and gives an outlook on possible future research topics to integrate explanations into everyday AI systems and thus enable the comprehensible handling of AI for all people.Seit den 1950er Jahren haben Anwendungen der Künstlichen Intelligenz (KI) die Menschen in ihren Bann gezogen. Diese Faszination wurde jedoch stets von Ernüchterung über die Grenzen dieser Technologie begleitet. Heute werden Methoden des maschinellen Lernens wie Deep Neural Networks (DNN) erfolgreich für verschiedene Aufgaben eingesetzt. Doch auch diese Methoden haben ihre Grenzen: Durch ihre Komplexität sind ihre Entscheidungen für den Menschen nicht mehr nachvollziehbar - sie sind Black-Boxes. Der Forschungszweig der Erklärbaren KI (engl. XAI) hat sich diesem Problem angenommen und untersucht, wie man KI-Entscheidungen nachvollziehbar machen kann. Dieser Wunsch ist nicht neu. In den 1970er Jahren beschäftigten sich die Entwickler von intrinsisch erklärbaren KI-Ansätzen, so genannten White-Boxes (z. B. regelbasierte Systeme), mit KI-Erklärungen. Heutzutage, mit dem zunehmenden Einsatz von KI-Systemen in allen Lebensbereichen, wird die Gestaltung nachvollziehbarer Systeme immer wichtiger. Die Entwicklung solcher Systeme ist Teil der Menschzentrierten KI (engl. HCAI) Forschung, die menschliche Bedürfnisse und Fähigkeiten in die Gestaltung von KI-Schnittstellen integriert. Dafür ist ein Verständnis darüber erforderlich, wie Menschen XAI wahrnehmen und wie KI-Erklärungen die Interaktion zwischen Mensch und KI beeinflussen. Eine der offenen Fragen betrifft die Untersuchung von XAI für Endnutzer, d.h. Menschen, die keine Expertise in KI haben, aber mit solchen Systemen interagieren oder von deren Entscheidungen betroffen sind. In dieser Dissertation wird untersucht, wie sich verschiedene Stufen interaktiver XAI von White- und Black-Box-KI-Systemen auf die Wahrnehmung der Endnutzer auswirken. Basierend auf einem interdisziplinären Konzept, das in dieser Arbeit vorgestellt wird, wird untersucht, wie der Inhalt, die Art und die Schnittstelle von Erklärungen von DNN (Black-Box) und regelbasierten Systemen (White-Box) von Endnutzern wahrgenommen werden. Wie XAI die mentalen Modelle, das Vertrauen, die Selbstwirksamkeit, die kognitive Belastung und den emotionalen Zustand der Endnutzer in Bezug auf das KI-System beeinflusst, steht im Mittelpunkt der Untersuchung. Zu Beginn der Arbeit werden allgemeine Konzepte zu KI, Erklärungen und psychologische Konstrukte von mentalen Modellen, Vertrauen, Selbstwirksamkeit, kognitiver Belastung und Emotionen vorgestellt. Anschließend werden verwandte Arbeiten bezüglich dem Design und der Untersuchung von XAI für Nutzer präsentiert. Diese dienen als Grundlage für das in dieser Dissertation vorgestellte Konzept einer Menschzentrierten Erklärbaren KI (engl. HC-XAI), das einen XAI-Designansatz mit Nutzerevaluationen kombiniert. Die Autorin verfolgt einen interdisziplinären Ansatz, der Wissen aus den Forschungsbereichen (X)AI, Mensch-Computer-Interaktion und Psychologie integriert. Auf der Grundlage dieses interdisziplinären Konzepts wird ein fünfstufiger Ansatz abgeleitet und im empirischen Teil dieser Arbeit auf exemplarische Umfragen und Experimente und angewendet. Zur Veranschaulichung der ersten beiden Schritte wird ein Persona-Ansatz für HC-XAI vorgestellt und darauf aufbauend eine Vorlage für den Entwurf von Personas bereitgestellt. Um die Verwendung der Vorlage zu veranschaulichen, werden drei Umfragen präsentiert, in denen Endnutzer zu ihren Einstellungen und Erwartungen gegenüber KI und XAI befragt werden. Die aus den Umfragedaten generierten Personas zeigen, dass es den Endnutzern oft an Wissen über XAI mangelt und dass ihre Wahrnehmung dessen von demografischen und persönlichkeitsbezogenen Merkmalen abhängt. Die Schritte drei bis fünf befassen sich mit der Gestaltung von XAI für konkrete Anwendungen. Hierzu werden verschiedene Stufen interaktiver XAI vorgestellt und in Experimenten mit Endanwendern untersucht. Zu diesem Zweck werden zwei regelbasierte Systeme (White-Box) und vier auf DNN basierende Systeme (Black-Box) verwendet. Diese werden für drei Zwecke eingesetzt: Kooperation & Kollaboration, Bildung und medizinische Entscheidungsunterstützung. Hierzu wurden sechs Nutzerstudien durchgeführt, die sich in der Interaktivität des verwendeten XAI-Systems unterschieden. Die Ergebnisse zeigen, dass das Vertrauen und die mentalen Modelle der Endnutzer in KI stark vom Nutzungskontext und der Gestaltung der Erklärung selbst abhängen. Es hat sich beispielsweise gezeigt, dass Erklärungen, die von einem virtuellen Agenten vermittelt werden, das Vertrauen fördern. Auch der Inhalt und die Art der Erklärungen werden von den Nutzern unterschiedlich wahrgenommen. Die Studien zeigen zudem, dass Endnutzer in unterschiedlichen Anwendungskontexten von XAI den Wunsch nach interaktiven Erklärungen verspüren. Die Dissertation schließt mit einer Zusammenfassung des wissenschaftlichen Beitrags, weist auf Grenzen der vorgestellten Arbeit hin und gibt einen Ausblick auf mögliche zukünftige Forschungsthemen, um Erklärungen in alltägliche KI-Systeme zu integrieren und damit den verständlichen Umgang mit KI für alle Menschen zu ermöglichen

Programming Languages and Systems

This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Dependent Object Types

A scalable programming language is one in which the same concepts can describe small as well as large parts. Towards this goal, Scala unifies concepts from object and module systems. In particular, objects can contain type members, which can be selected as types, called path-dependent types. Focusing on path-dependent types, we develop a type-theoretic foundation for Scala: the calculus of Dependent Object Types (DOT). We derive DOT from System F, we add a lower bound to each type variable, in addition to its usual upper bound, (2) in System D, we turn each type variable into a regular term variable containing a type, (3) for a full subtyping lattice, we add intersection and union types, (4) for objects, we consolidate all values into records, (5) for objects that close over a self, we introduce a recursive type, binding a self term variable, (6) for recursive types, we first extend the theory in typing and then also in subtyping. Through this bottom-up exploration, we discover a sound, uniform yet powerful design for DOT. We devise strategies and techniques for proving soundness that scale through this iterative step-by-step process: (1) "pushback" of subtyping transitivity or subsumption, to concisely capture inversion of subtyping or typing, (2) distinction between concrete vs. abstract context variables, to resolve tension between preservation of types vs. preservation of type abstractions, (3) and, specifically for big-step semantics, a type that closes over an environment, to relate context-dependent types across closures. While ultimately, we have developed sound models of DOT in both big-step and small-step operational semantics, historically, the shift to big-step semantics has been helpful in focusing the requirements. In particular, by developing a novel big-step soundness proof for System F<:, calculi like System D<: emerge as straightforward generalizations, almost like removing artificial restrictions. Interesting in their own right, our type soundness techniques for definitional interpreters extend to mutable references without use of co-induction. The DOT calculus finally grounds languages like Scala in firm theory. The DOT calculus helps in finding bugs in Scala, and in understanding feature interaction better as well as requirements. The DOT calculus serves as a good basis for future work which studies extensions or encodings on top of the core, bridging the gap from DOT to Dotty / Scala

New Graph Algorithms via Polyhedral Techniques

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. Somewhat surprisingly, similar polyhedral techniques can be harnessed in the two seemingly disparate settings. In the first part of the thesis we address a benchmark problem in combinatorial optimization: the asymmetric traveling salesman problem (ATSP). It consists in finding the shortest tour that visits all vertices of a given directed graph with weights on edges. Due to its NP-hardness, the theoretical study of algorithms for ATSP has focused on approximation algorithms: ones that are provably both efficient and give solutions competitive with the optimum. Specifically, a rho-approximation algorithm for ATSP is one that runs in polynomial time and always outputs a tour that is at most rho times longer than the shortest tour. Finding such an approximation algorithm with rho bounded (i.e., a constant factor) had been a long-standing open problem. In this thesis, we give such an algorithm. Our approximation guarantee is analyzed with respect to the standard linear programming relaxation, and thus our result also confirms the conjectured constant integrality gap of that relaxation. Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics due to Svensson. In particular, we give a generic reduction to structured instances that resemble but are more general than those arising from node-weighted metrics. This reduction takes advantage of a laminar family of vertex sets that arises from the linear programming relaxation. In the second part of the thesis we address the perfect matching problem. The first polynomial-time algorithm for it, given by Edmonds in 1965, is historically associated with the introduction of the class P and our notion that ``polynomial-time'' means ``efficient''. That algorithm is sequential and deterministic. We have also known since the 1980s that the matching problem has efficient parallel algorithms if the use of randomness is allowed. Formally, it is in the class RNC, i.e., it has randomized algorithms that use polynomially many processors and run in polylogarithmic time. However, we do not know if randomness is necessary - that is, whether the matching problem is in the class NC. In this thesis we show that the matching problem is in quasi-NC. That is, we give a deterministic parallel algorithm that runs in O(log^3 n) time on n^{O(log^2 n)} processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the classic paper by Mulmuley, Vazirani and Vazirani to obtain an RNC algorithm. Our proof extends the framework of Fenner, Gurjar and Thierauf, who proved the analogous result in the special case of bipartite graphs. Compared to that setting, several new ingredients are needed due to the significantly more complex structure of perfect matchings in general graphs. In particular, our proof heavily relies on the laminar structure of the faces of the perfect matching polytope