Concurrent Kleene Algebra: Free Model and Completeness

Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and Wehrman in 2009 as a framework to reason about concurrent programs. We prove that the axioms for CKA with bounded parallelism are complete for the semantics proposed in the original paper; consequently, these semantics are the free model for this fragment. This result settles a conjecture of Hoare and collaborators. Moreover, the techniques developed along the way are reusable; in particular, they allow us to establish pomset automata as an operational model for CKA.Comment: Version 2 includes an overview section that outlines the completeness proof, as well as some extra discussion of the interpolation lemma. It also includes better typography and a number of minor fixes. Version 3 incorporates the changes by comments from the anonymous referees at ESOP. Among other things, these include a worked example of computing the syntactic closure by han

Quantitative Modeling and Verification of Evolving Software

Mit der steigenden Nachfrage nach Innovationen spielt Software in verschiedenenWirtschaftsbereichen eine wichtige Rolle, wie z.B. in der Automobilindustrie, bei intelligenten Systemen als auch bei Kommunikationssystemen. Daher ist die Qualität für die Softwareentwicklung von großer Bedeutung. Allerdings ändern sich die probabilistische Modelle (die Qualitätsbewertungsmodelle) angesichts der dynamischen Natur moderner Softwaresysteme. Dies führt dazu, dass ihre Übergangswahrscheinlichkeiten im Laufe der Zeit schwanken, welches zu erheblichen Problemen führt. Dahingehend werden probabilistische Modelle im Hinblick auf ihre Laufzeit kontinuierlich aktualisiert. Eine fortdauernde Neubewertung komplexer Wahrscheinlichkeitsmodelle ist jedoch teuer. In letzter Zeit haben sich inkrementelle Ansätze als vielversprechend für die Verifikation von adaptiven Systemen erwiesen. Trotzdem wurden bei der Bewertung struktureller Änderungen im Modell noch keine wesentlichen Verbesserungen erzielt. Wahrscheinlichkeitssysteme werden als Automaten modelliert, wie bei Markov-Modellen. Solche Modelle können in Matrixform dargestellt werden, um die Gleichungen basierend auf Zuständen und Übergangswahrscheinlichkeiten zu lösen. Laufzeitmodelle wie Matrizen sind nicht signifikant, um die Auswirkungen von Modellveränderungen erkennen zu können. In dieser Arbeit wird ein Framework unter Verwendung stochastischer Bäume mit regulären Ausdrücken entwickelt, welches modular aufgebaut ist und eine aktionshaltige sowie probabilistische Logik im Kontext der Modellprüfung aufweist. Ein solches modulares Framework ermöglicht dem Menschen die Entwicklung der Änderungsoperationen für die inkrementelle Berechnung lokaler Änderungen, die im Modell auftreten können. Darüber hinaus werden probabilistische Änderungsmuster beschrieben, um eine effiziente inkrementelle Verifizierung, unter Verwendung von Bäumen mit regulären Ausdrücken, anwenden zu können. Durch die Bewertung der Ergebnisse wird der Vorgang abgeschlossen.Software plays an innovative role in many different domains, such as car industry, autonomous and smart systems, and communication. Hence, the quality of the software is of utmost importance and needs to be properly addressed during software evolution. Several approaches have been developed to evaluate systems’ quality attributes, such as reliability, safety, and performance of software. Due to the dynamic nature of modern software systems, probabilistic models representing the quality of the software and their transition probabilities change over time and fluctuate, leading to a significant problem that needs to be solved to obtain correct evaluation results of quantitative properties. Probabilistic models need to be continually updated at run-time to solve this issue. However, continuous re-evaluation of complex probabilistic models is expensive. Recently, incremental approaches have been found to be promising for the verification of evolving and self-adaptive systems. Nevertheless, substantial improvements have not yet been achieved for evaluating structural changes in the model. Probabilistic systems are usually represented in a matrix form to solve the equations based on states and transition probabilities. On the other side, evolutionary changes can create various effects on theese models and force them to re-verify the whole system. Run-time models, such as matrices or graph representations, lack the expressiveness to identify the change effect on the model. In this thesis, we develop a framework using stochastic regular expression trees, which are modular, with action-based probabilistic logic in the model checking context. Such a modular framework enables us to develop change operations for the incremental computation of local changes that can occur in the model. Furthermore, we describe probabilistic change patterns to apply efficient incremental quantitative verification using stochastic regular expression trees and evaluate our results

Search-Based Regular Expression Inference on a GPU

Regular expression inference (REI) is a supervised machine learning and program synthesis problem that takes a cost metric for regular expressions, and positive and negative examples of strings as input. It outputs a regular expression that is precise (i.e., accepts all positive and rejects all negative examples), and minimal w.r.t. to the cost metric. We present a novel algorithm for REI over arbitrary alphabets that is enumerative and trades off time for space. Our main algorithmic idea is to implement the search space of regular expressions succinctly as a contiguous matrix of bitvectors. Collectively, the bitvectors represent, as characteristic sequences, all sub-languages of the infix-closure of the union of positive and negative examples. Mathematically, this is a semiring of (a variant of) formal power series. Infix-closure enables bottom-up compositional construction of larger from smaller regular expressions using the operations of our semiring. This minimises data movement and data-dependent branching, hence maximises data-parallelism. In addition, the infix-closure remains unchanged during the search, hence search can be staged: first pre-compute various expensive operations, and then run the compute intensive search process. We provide two C++ implementations, one for general purpose CPUs and one for Nvidia GPUs (using CUDA). We benchmark both on Google Colab Pro: the GPU implementation is on average over 1000x faster than the CPU implementation on the hardest benchmarks

ZStream: A cost-based query processor for adaptively detecting composite events

Composite (or Complex) event processing (CEP) systems search sequences of incoming events for occurrences of user-specified event patterns. Recently, they have gained more attention in a variety of areas due to their powerful and expressive query language and performance potential. Sequentiality (temporal ordering) is the primary way in which CEP systems relate events to each other. In this paper, we present a CEP system called ZStream to efficiently process such sequential patterns. Besides simple sequential patterns, ZStream is also able to detect other patterns, including conjunction, disjunction, negation and Kleene closure. Unlike most recently proposed CEP systems, which use non-deterministic finite automata (NFA's) to detect patterns, ZStream uses tree-based query plans for both the logical and physical representation of query patterns. By carefully designing the underlying infrastructure and algorithms, ZStream is able to unify the evaluation of sequence, conjunction, disjunction, negation, and Kleene closure as variants of the join operator. Under this framework, a single pattern in ZStream may have several equivalent physical tree plans, with different evaluation costs. We propose a cost model to estimate the computation costs of a plan. We show that our cost model can accurately capture the actual runtime behavior of a plan, and that choosing the optimal plan can result in a factor of four or more speedup versus an NFA based approach. Based on this cost model and using a simple set of statistics about operator selectivity and data rates, ZStream is able to adaptively and seamlessly adjust the order in which it detects patterns on the fly. Finally, we describe a dynamic programming algorithm used in our cost model to efficiently search for an optimal query plan for a given pattern.National Natural Science Foundation (Grant number NETS-NOSS 0520032

Heap Abstractions for Static Analysis

Heap data is potentially unbounded and seemingly arbitrary. As a consequence, unlike stack and static memory, heap memory cannot be abstracted directly in terms of a fixed set of source variable names appearing in the program being analysed. This makes it an interesting topic of study and there is an abundance of literature employing heap abstractions. Although most studies have addressed similar concerns, their formulations and formalisms often seem dissimilar and some times even unrelated. Thus, the insights gained in one description of heap abstraction may not directly carry over to some other description. This survey is a result of our quest for a unifying theme in the existing descriptions of heap abstractions. In particular, our interest lies in the abstractions and not in the algorithms that construct them. In our search of a unified theme, we view a heap abstraction as consisting of two features: a heap model to represent the heap memory and a summarization technique for bounding the heap representation. We classify the models as storeless, store based, and hybrid. We describe various summarization techniques based on k-limiting, allocation sites, patterns, variables, other generic instrumentation predicates, and higher-order logics. This approach allows us to compare the insights of a large number of seemingly dissimilar heap abstractions and also paves way for creating new abstractions by mix-and-match of models and summarization techniques.Comment: 49 pages, 20 figure

Entwurf funktionaler Implementierungen von Graphalgorithmen

Classic graph algorithms are usually presented and analysed in imperative programming languages. Imperative programming languages are well-suited for the description of a program flow, in which the order in which the operations are performed is important. One common example of such a description is the successive, typically destructive modification of objects. This kind of iteration often occurs in the context of graph algorithms that deal with a certain kind of optimisation. In functional programming, the order of execution is abstracted and problem solutions are described as compositions of intermediate solutions. Additionally, functional programming languages are referentially transparent and thus destructive updates of objects are discouraged. The development of purely functional graph algorithms begins with the decomposition of a given problem into simpler problems. In many cases the solutions of these partial problems can be used to solve different problems as well. What is more, this compositionality allows exchanging functions for more efficient or more comprehensible versions with little effort. An algebraic approach with a focus on relation algebra as defined by Tarski is used as an intermediate step in this dissertation. One advantage of this approach is the formality of the resulting specifications. Despite their formality, the resulting expressions are still readable, because the algebraic operations have intuitive interpretations. Another advantage is that the specification is executable, once the necessary operations are implemented. This dissertation presents the basics of the algebraic approach in the functional programming language Haskell. Using this foundation, some exemplary graph-theoretic problems are solved in the presented framework. Finally, optimisations of the presented implementations are discussed and pointers are provided to further problems that can be solved using the above methods.Klassische Graphalgorithmen werden üblicherweise in imperativen Programmiersprachen beschrieben und analysiert. Imperative Programmiersprachen eignen sich gut, um Programmabläufe zu beschreiben, in welchen die Reihenfolge der Operationen wichtig ist. Dies betrifft insbesondere die schrittweise, in der Regel destruktive Veränderung von Objekten, wie sie häufig im Falle von Optimierungsproblemen auf Graphen vorkommt. In der funktionalen Programmierung abstrahiert man von einer festen Berechnungsreihenfolge und beschreibt Problemlösungen als Kompositionen von Teillösungen. Ferner sind funktionale Programmiersprachen referentiell transparent, sodass destruktive Veränderungen nur bedingt möglich sind. Die Entwicklung rein funktionaler Graphalgorithmen setzt bei der Zerlegung der bestehenden Probleme in einfachere Probleme an. Oftmals können Lösungen dieser Teilprobleme auch in anderen Situationen eingesetzt werden. Darüber hinaus erlaubt es diese Kompositionalität, einzelne Funktionen mit wenig Aufwand durch effizientere oder verständlichere Fassungen auszutauschen. Als Zwischenschritt in der Entwicklung wird in dieser Dissertation ein algebraischer Ansatz basierend auf der Relationenalgebra im Sinne von Tarski verwendet. Ein Vorteil dieses Ansatzes ist die Formalität der entstehenden Spezifikationen. Trotz ihrer Formalität bleiben die entstehenden Ausdrücke oft leserlich, weil die algebraischen Operationen anschauliche Interpretationen zulassen. Ein weiterer Vorteil ist, dass Spezifikationen ausführbar werden, sobald bestimmte Basisoperationen implementiert sind. In dieser Dissertation werden Grundlagen einer Implementierung des algebraischen Ansatzes in der funktionalen Programmiersprache Haskell behandelt. Ausgehend hiervon werden exemplarisch einige Probleme der Graphentheorie gelöst. Schließlich werden Optimierungen der vorgestellten Implementierungen und weitere Probleme, welche mit den obigen Methoden lösbar sind, diskutiert