296 research outputs found
Parameter-Independent Strategies for pMDPs via POMDPs
Markov Decision Processes (MDPs) are a popular class of models suitable for
solving control decision problems in probabilistic reactive systems. We
consider parametric MDPs (pMDPs) that include parameters in some of the
transition probabilities to account for stochastic uncertainties of the
environment such as noise or input disturbances.
We study pMDPs with reachability objectives where the parameter values are
unknown and impossible to measure directly during execution, but there is a
probability distribution known over the parameter values. We study for the
first time computing parameter-independent strategies that are expectation
optimal, i.e., optimize the expected reachability probability under the
probability distribution over the parameters. We present an encoding of our
problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem
to computing optimal strategies in POMDPs.
We evaluate our method experimentally on several benchmarks: a motivating
(repeated) learner model; a series of benchmarks of varying configurations of a
robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape
PrIC3: Property Directed Reachability for MDPs
IC3 has been a leap forward in symbolic model checking. This paper proposes
PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic
model checking of MDPs. Our main focus is to develop the theory underlying
PrIC3. Alongside, we present a first implementation of PrIC3 including the key
ingredients from IC3 such as generalization, repushing, and propagation
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
Model reduction techniques for probabilistic verification of Markov chains
Probabilistic model checking is a quantitative verification technique that aims to verify the correctness of probabilistic systems. Nevertheless, it suffers from the so-called state space explosion problem. In this thesis, we propose two new model reduction techniques to improve the efficiency and scalability of verifying probabilistic systems, focusing on discrete-time Markov chains (DTMCs). In particular, our emphasis is on verifying quantitative properties that bound the time or cost of an execution. We also focus on methods that avoid the explicit construction of the full state space.
We first present a finite-horizon variant of probabilistic bisimulation for DTMCs, which preserves a bounded fragment of PCTL. We also propose another model reduction technique that reduces what we call linear inductive DTMCs, a class of models whose state space grows linearly with respect to a parameter.
All the techniques presented in this thesis were developed in the PRISM model checker. We demonstrate the effectiveness of our work by applying it to a selection of existing benchmark probabilistic models, showing that both of our two new approaches can provide significant reductions in model size and in some cases outperform the existing implementations of probabilistic verification in PRISM
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Lower Bounds for Possibly Divergent Probabilistic Programs
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish non-trivial lower bounds on, e.g., termination probabilities and expected values, for possibly divergent probabilistic loops, e.g., the well-known three-dimensional random walk on a lattice
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