IST Austria Thesis

This dissertation focuses on algorithmic aspects of program verification, and presents modeling and complexity advances on several problems related to the static analysis of programs, the stateless model checking of concurrent programs, and the competitive analysis of real-time scheduling algorithms. Our contributions can be broadly grouped into five categories. Our first contribution is a set of new algorithms and data structures for the quantitative and data-flow analysis of programs, based on the graph-theoretic notion of treewidth. It has been observed that the control-flow graphs of typical programs have special structure, and are characterized as graphs of small treewidth. We utilize this structural property to provide faster algorithms for the quantitative and data-flow analysis of recursive and concurrent programs. In most cases we make an algebraic treatment of the considered problem, where several interesting analyses, such as the reachability, shortest path, and certain kind of data-flow analysis problems follow as special cases. We exploit the constant-treewidth property to obtain algorithmic improvements for on-demand versions of the problems, and provide data structures with various tradeoffs between the resources spent in the preprocessing and querying phase. We also improve on the algorithmic complexity of quantitative problems outside the algebraic path framework, namely of the minimum mean-payoff, minimum ratio, and minimum initial credit for energy problems. Our second contribution is a set of algorithms for Dyck reachability with applications to data-dependence analysis and alias analysis. In particular, we develop an optimal algorithm for Dyck reachability on bidirected graphs, which are ubiquitous in context-insensitive, field-sensitive points-to analysis. Additionally, we develop an efficient algorithm for context-sensitive data-dependence analysis via Dyck reachability, where the task is to obtain analysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is (i)~linear in the number of call sites and (ii)~only logarithmic in the size of the whole library, as opposed to linear in the size of the whole library. Finally, we prove that Dyck reachability is Boolean Matrix Multiplication-hard in general, and the hardness also holds for graphs of constant treewidth. This hardness result strongly indicates that there exist no combinatorial algorithms for Dyck reachability with truly subcubic complexity. Our third contribution is the formalization and algorithmic treatment of the Quantitative Interprocedural Analysis framework. In this framework, the transitions of a recursive program are annotated as good, bad or neutral, and receive a weight which measures the magnitude of their respective effect. The Quantitative Interprocedural Analysis problem asks to determine whether there exists an infinite run of the program where the long-run ratio of the bad weights over the good weights is above a given threshold. We illustrate how several quantitative problems related to static analysis of recursive programs can be instantiated in this framework, and present some case studies to this direction. Our fourth contribution is a new dynamic partial-order reduction for the stateless model checking of concurrent programs. Traditional approaches rely on the standard Mazurkiewicz equivalence between traces, by means of partitioning the trace space into equivalence classes, and attempting to explore a few representatives from each class. We present a new dynamic partial-order reduction method called the Data-centric Partial Order Reduction (DC-DPOR). Our algorithm is based on a new equivalence between traces, called the observation equivalence. DC-DPOR explores a coarser partitioning of the trace space than any exploration method based on the standard Mazurkiewicz equivalence. Depending on the program, the new partitioning can be even exponentially coarser. Additionally, DC-DPOR spends only polynomial time in each explored class. Our fifth contribution is the use of automata and game-theoretic verification techniques in the competitive analysis and synthesis of real-time scheduling algorithms for firm-deadline tasks. On the analysis side, we leverage automata on infinite words to compute the competitive ratio of real-time schedulers subject to various environmental constraints. On the synthesis side, we introduce a new instance of two-player mean-payoff partial-information games, and show how the synthesis of an optimal real-time scheduler can be reduced to computing winning strategies in this new type of games

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

A Formal Model of Ambiguity and its Applications in Machine Translation

Systems that process natural language must cope with and resolve ambiguity. In this dissertation, a model of language processing is advocated in which multiple inputs and multiple analyses of inputs are considered concurrently and a single analysis is only a last resort. Compared to conventional models, this approach can be understood as replacing single-element inputs and outputs with weighted sets of inputs and outputs. Although processing components must deal with sets (rather than individual elements), constraints are imposed on the elements of these sets, and the representations from existing models may be reused. However, to deal efficiently with large (or infinite) sets, compact representations of sets that share structure between elements, such as weighted finite-state transducers and synchronous context-free grammars, are necessary. These representations and algorithms for manipulating them are discussed in depth in depth. To establish the effectiveness and tractability of the proposed processing model, it is applied to several problems in machine translation. Starting with spoken language translation, it is shown that translating a set of transcription hypotheses yields better translations compared to a baseline in which a single (1-best) transcription hypothesis is selected and then translated, independent of the translation model formalism used. More subtle forms of ambiguity that arise even in text-only translation (such as decisions conventionally made during system development about how to preprocess text) are then discussed, and it is shown that the ambiguity-preserving paradigm can be employed in these cases as well, again leading to improved translation quality. A model for supervised learning that learns from training data where sets (rather than single elements) of correct labels are provided for each training instance and use it to learn a model of compound word segmentation is also introduced, which is used as a preprocessing step in machine translation

Metastability-containing circuits, parallel distance problems, and terrain guarding

We study three problems. The first is the phenomenon of metastability in digital circuits. This is a state of bistable storage elements, such as registers, that is neither logical 0 nor 1 and breaks the abstraction of Boolean logic. We propose a time- and value-discrete model for metastability in digital circuits and show that it reflects relevant physical properties. Further, we propose the fundamentally new approach of using logical masking to perform meaningful computations despite the presence of metastable upsets and analyze what functions can be computed in our model. Additionally, we show that circuits with masking registers grow computationally more powerful with each available clock cycle. The second topic are parallel algorithms, based on an algebraic abstraction of the Moore-Bellman-Ford algorithm, for solving various distance problems. Our focus are distance approximations that obey the triangle inequality while at the same time achieving polylogarithmic depth and low work. Finally, we study the continuous Terrain Guarding Problem. We show that it has a rational discretization with a quadratic number of guard candidates, establish its membership in NP and the existence of a PTAS, and present an efficient implementation of a solver.Wir betrachten drei Probleme, zunächst das Phänomen von Metastabilität in digitalen Schaltungen. Dabei geht es um einen Zustand in bistabilen Speicherelementen, z.B. Registern, welcher weder logisch 0 noch 1 entspricht und die Abstraktion Boolescher Logik unterwandert. Wir präsentieren ein zeit- und wertdiskretes Modell für Metastabilität in digitalen Schaltungen und zeigen, dass es relevante physikalische Eigenschaften abbildet. Des Weiteren präsentieren wir den grundlegend neuen Ansatz, trotz auftretender Metastabilität mit Hilfe von logischem Maskieren sinnvolle Berechnungen durchzuführen und bestimmen, welche Funktionen in unserem Modell berechenbar sind. Darüber hinaus zeigen wir, dass durch Maskingregister in zusätzlichen Taktzyklen mehr Funktionen berechenbar werden. Das zweite Thema sind parallele Algorithmen die, basierend auf einer Algebraisierung des Moore-Bellman-Ford-Algorithmus, diverse Distanzprobleme lösen. Der Fokus liegt auf Distanzapproximationen unter Einhaltung der Dreiecksungleichung bei polylogarithmischer Tiefe und niedriger Arbeit. Abschließend betrachten wir das kontinuierliche Terrain Guarding Problem. Wir zeigen, dass es eine rationale Diskretisierung mit einer quadratischen Anzahl von Wächterpositionen erlaubt, folgern dass es in NP liegt und ein PTAS existiert und präsentieren eine effiziente Implementierung, die es löst