Towards the Formal Reliability Analysis of Oil and Gas Pipelines

It is customary to assess the reliability of underground oil and gas pipelines in the presence of excessive loading and corrosion effects to ensure a leak-free transport of hazardous materials. The main idea behind this reliability analysis is to model the given pipeline system as a Reliability Block Diagram (RBD) of segments such that the reliability of an individual pipeline segment can be represented by a random variable. Traditionally, computer simulation is used to perform this reliability analysis but it provides approximate results and requires an enormous amount of CPU time for attaining reasonable estimates. Due to its approximate nature, simulation is not very suitable for analyzing safety-critical systems like oil and gas pipelines, where even minor analysis flaws may result in catastrophic consequences. As an accurate alternative, we propose to use a higher-order-logic theorem prover (HOL) for the reliability analysis of pipelines. As a first step towards this idea, this paper provides a higher-order-logic formalization of reliability and the series RBD using the HOL theorem prover. For illustration, we present the formal analysis of a simple pipeline that can be modeled as a series RBD of segments with exponentially distributed failure times.Comment: 15 page

Performance Analysis and Functional Verification of the Stop-and-Wait Protocol in HOL

Real-time systems usually involve a subtle interaction of a number of distributed components and have a high degree of parallelism, which makes their performance analysis quite complex. Thus, traditional techniques, such as simulation, or the state-based formal methods usually fail to produce reasonable results. In this paper, we propose to use higher-order-logic (HOL) theorem proving for the performance analysis of real-time systems. The idea is to formalize the real-time system as a logical conjunction of HOL predicates, whereas each one of these predicates define an autonomous component or process of the given real-time system. The random or unpredictable behavior found in these components is modeled as random variables. This formal specification can then be used in a HOL theorem prover to reason about both functional and performance related properties of the given real-time system. In order to illustrate the practical effectiveness of our approach, we present the analysis of the Stop-and-Wait protocol, which is a classical example of real-time systems. The functional correctness of the protocol is verified by proving that the protocol ensures reliable data transfers. Whereas, the average message delay relation is verified in HOL for the sake of performance analysis. The paper includes the protocol’s formalization details along with the HOL proof sketches for the major theorems

Probabilistic Analysis of Wireless Systems Using Theorem Proving

Probabilistic techniques play a major role in the design and analysis of wirelesssystems as they contain a significant amount of random or unpredictable components. Traditionally, computer simulation techniques are used to perform probabilisticanalysis of wirelesssystems but they provide inaccurate results and usually require enormous amount of CPU time in order to attain reasonable estimates. To overcome these limitations, we propose to use a higher-order-logic theorem prover (HOL) for the analysis of wirelesssystems. The paper presents a concise description of the formal foundations required to conduct the analysis of a wirelesssystem in a theorem prover, such as the higher-order-logic modeling of random variables and the verification of their corresponding probabilistic and statistical properties in a theorem prover. In order to illustrate the utilization and effectiveness of the proposed idea for handling real-world wirelesssystemanalysis problems, we present an analysis of the automated repeat request (ARQ) mechanism at the logic link control (LLC) layer of the General Packet Radio Service (GPRS), which is a packet oriented mobile data service available to the users of Global System for Mobile Communications (GSM)

Reasoning about conditional probabilities in a higher-order-logic theorem prover

In the field of probabilistic analysis, the concept of conditionalprobability plays a major role for estimating probabilities when some partial information concerning the result of the experiment is available. This paper presents ahigher-order-logic definition of conditionalprobability and the formal verification of some classical properties of conditionalprobability, such as, the total probability law and Bayes' theorem. This infrastructure, implemented in the HOL theoremprover, allows us to precisely reason about conditionalprobabilities for probabilistic systems within the sound core of HOL and thus proves to be quite useful for the analysis of systems used in safety-critical domains, such as space, medicine and transportation. To demonstrate the usefulness of our approach, we provide the precise probabilistic analysis of the binary asymmetric channel, a widely used concept in communication theory, within the HOL theoremprover

Formally Analyzing Expected Time Complexity of Algorithms Using Theorem Proving

Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem. Traditionally, such analyses are performed using paper-and-pencil proofs and the results are sometimes validated using simulation techniques. These techniques are informal and thus may result in an inaccurate analysis. In this paper, we propose a formal technique for analyzing the expected time complexity of algorithms using higher-order-logic theorem proving. The approach calls for mathematically modeling the algorithm along with its inputs, using indicator random variables, in higher-order logic. This model is then used to formally reason about the expected time complexity of the underlying algorithm in a theorem prover. The paper includes the higher-order-logic formalization of indicator random variables, which are fundamental to the proposed infrastructure. In order to illustrate the practical effectiveness and utilization of the proposed infrastructure, the paper also includes the analysis of algorithms for three well-known problems, i.e., the hat-check problem, the birthday paradox and the hiring problem

Formal verification of a fault tolerant clock synchronization algorithm

A formal specification and mechanically assisted verification of the interactive convergence clock synchronization algorithm of Lamport and Melliar-Smith is described. Several technical flaws in the analysis given by Lamport and Melliar-Smith were discovered, even though their presentation is unusally precise and detailed. It seems that these flaws were not detected by informal peer scrutiny. The flaws are discussed and a revised presentation of the analysis is given that not only corrects the flaws but is also more precise and easier to follow. Some of the corrections to the flaws require slight modifications to the original assumptions underlying the algorithm and to the constraints on its parameters, and thus change the external specifications of the algorithm. The formal analysis of the interactive convergence clock synchronization algorithm was performed using the Enhanced Hierarchical Development Methodology (EHDM) formal specification and verification environment. This application of EHDM provides a demonstration of some of the capabilities of the system

Intégration des méthodes formelles dans le développement des RCSFs

In this thesis, we have relied on formal techniques in order to first evaluate WSN protocols and then to propose solutions that meet the requirements of these networks. The thesis contributes to the modelling, analysis, design and evaluation of WSN protocols. In this context, the thesis begins with a survey on WSN and formal verification techniques. Focusing on the MAC layer, the thesis reviews proposed MAC protocols for WSN as well as their design challenges. The dissertation then proceeds to outline the contributions of this work. As a first proposal, we develop a stochastic generic model of the 802.11 MAC protocol for an arbitrary network topology and then perform probabilistic evaluation of the protocol using statistical model checking. Considering an alternative power source to operate WSN, energy harvesting, we move to the second proposal where a protocol designed for EH-WSN is modelled and various performance parameters are evaluated. Finally, the thesis explores mobility in WSN and proposes a new MAC protocol, named "Mobility and Energy Harvesting aware Medium Access Control (MEH-MAC)" protocol for dynamic sensor networks powered by ambient energy. The protocol is modelled and verified under several features