An Event Structure Model for Probabilistic Concurrent Kleene Algebra

We give a new true-concurrent model for probabilistic concurrent Kleene algebra. The model is based on probabilistic event structures, which combines ideas from Katoen's work on probabilistic concurrency and Varacca's probabilistic prime event structures. The event structures are compared with a true-concurrent version of Segala's probabilistic simulation. Finally, the algebraic properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules.Comment: Submitted and accepted for LPAR19 (2013

Algebraic Verification of Probabilistic and Concurrent Systems

This thesis provides an algebraic modelling and verification of probabilistic concurrent systems in the style of Kleene algebra. Without concurrency, it is shown that the equational theory of continuous probabilistic Kleene algebra is complete with respect to an automata model under standard simulation equivalence. This yields a minimisation-based decision procedure for the algebra. Without probability, an event structure model of Hoare et al.'s concurrent Kleene algebra is constructed. These two algebras are then ``merged" to provide probabilistic concurrent Kleene algebra which is used to discover and prove development rules for probabilistic concurrent systems (e.g. rely/guarantee calculus). Soundness of the new algebra is ensured by models based on probabilistic automata (interleaving) and probabilistic bundle event structures (true concurrency) quotiented with the respective simulation equivalences. Lastly, event structures with implicit probabilities are constructed to provide a state based model for the soundness of the probabilistic rely/guarantee rules

Probabilistic Rely-guarantee Calculus

Jones' rely-guarantee calculus for shared variable concurrency is extended to include probabilistic behaviours. We use an algebraic approach which combines and adapts probabilistic Kleene algebras with concurrent Kleene algebra. Soundness of the algebra is shown relative to a general probabilistic event structure semantics. The main contribution of this paper is a collection of rely-guarantee rules built on top of that semantics. In particular, we show how to obtain bounds on probabilities by deriving rely-guarantee rules within the true-concurrent denotational semantics. The use of these rules is illustrated by a detailed verification of a simple probabilistic concurrent program: a faulty Eratosthenes sieve.Comment: Preprint submitted to TCS-QAP

On Kleene Algebra vs. Process Algebra

We try to clarify the relationship between Kleene algebra and process algebra, based on the very recent work on Kleene algebra and process algebra. Both for concurrent Kleene algebra (CKA) with communications and truly concurrent process algebra APTC with Kleene star and parallel star, the extended Milner's expansion law $a\parallel b=a\cdot b+b\cdot a+a\parallel b +a\mid b$ holds, with $a,b$ being primitives (atomic actions), $\parallel$ being the parallel composition, $+$ being the alternative composition, $\cdot$ being the sequential composition and the communication merge $\mid$ with the background of computation. CKA and APTC are all the truly concurrent computation models, can have the same syntax (primitives and operators), maybe have the same or different semantics

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

Probabilistic Concurrent Kleene Algebra

We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of probabilistic automata modulo probabilistic simulation. We use the resulting algebra to generalise the algebraic formulation of a variant of Jones' rely/guarantee calculus