Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Value Iteration for Long-run Average Reward in Markov Decision Processes

Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks

On Role Logic

We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of first-order logic in lambda calculus, and a simple rule for implicit arguments of unary and binary predicates. The unrestricted version of role logic has the expressive power of first-order logic with transitive closure. Using a syntactic restriction on role logic formulas, we identify a natural fragment RL^2 of role logic. We show that the RL^2 fragment has the same expressive power as two-variable logic with counting C^2 and is therefore decidable. We present a translation of an imperative language into the decidable fragment RL^2, which allows compositional verification of programs that manipulate relational structures. In addition, we show how RL^2 encodes boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor

Foundations of the B method

B is a method for specifying, designing and coding software systems. It is based on Zermelo-Fraenkel set theory with the axiom of choice, the concept of generalized substitution and on structuring mechanisms (machine, refinement, implementation). The concept of refinement is the key notion for developing B models of (software) systems in an incremental way. B models are accompanied by mathematical proofs that justify them. Proofs of B models convince the user (designer or specifier) that the (software) system is effectively correct. We provide a survey of the underlying logic of the B method and the semantic concepts related to the B method; we detail the B development process partially supported by the mechanical engine of the prover

A static analysis for quantifying information flow in a simple imperative language

We propose an approach to quantify interference in a simple imperative language that includes a looping construct. In this paper we focus on a particular case of this definition of interference: leakage of information from private variables to public ones via a Trojan Horse attack. We quantify leakage in terms of Shannon's information theory and we motivate our definition by proving a result relating this definition of leakage and the classical notion of programming language interference. The major contribution of the paper is a quantitative static analysis based on this definition for such a language. The analysis uses some non-trivial information theory results like Fano's inequality and L1 inequalities to provide reasonable bounds for conditional statements. While-loops are handled by integrating a qualitative flow-sensitive dependency analysis into the quantitative analysis

Continuous probability distributions in model-based specification languages

PhD ThesisModel-based speci cation languages provide a means for obtaining assurance of dependability of complex computer-based systems, but provide little support for modelling and analysing fault behaviour, which is inherently probabilistic in nature. In particular, the need for a detailed account of the role of continuous probability has been largely overlooked. This thesis addresses the role of continuous probability in model-based speci cation languages. A model-based speci cation language (sGCL) that supports continuous probability distributions is de ned. The use of sGCL and how it interacts with engineering practices is also explored. In addition, a re nement ordering for continuous probability distributions is given, and the challenge of combining non-determinism and continuous probability is discussed in depth. The thesis is presented in three parts. The rst uses two case studies to explore the use of probability in formal methods. The rst case study, on ash memory, is used to present the capabilities of probabilistic formal methods and to determine the kinds of questions that require continuous probability distributions to answer. The second, on an emergency brake system, illustrates the strengths and weaknesses of existing languages and provides a basis for exploring a prototype language that includes continuous probability. The second part of the thesis gives the formal de nition of sGCL's syntax and semantics. The semantics is made up of two parts, the proof theory (transformer semantics) and the underpinning mathematics (relational semantics). The additional language constructs and semantical features required to include non-determinism as well as continuous probability are also discussed. The most challenging aspect lies in proving the consistency of the semantics when non-determinism is also included. The third part uses a nal case study, on an aeroplane pitch monitor, to demonstrate the use of sGCL. The new analysis techniques provided by sGCL, and how they t in with engineering practices, are explored.EPSRC: The School of Computing Science, Newcastle University: DEPLOY project

Stepwise Development Of Distributed Vertex Coloring Algorithms (Full Report)

Software-based systems have a strong impact in the daily life. For instance, systems like televisions, cell phones, credit cards are used for persons, while others systems, like networks, telecommunications, distributed and embedded devices, supercomputers, are used by organisations such as companies, governments, nations... Several countries, especially the advanced ones, rely on systems for the efficiency of domains like economy, health... Since they are needed in daily life, those systems should be reliable, and their specifications and design must be clear, understandable and should follow specific rules and they must avoid faults, failures and if they can not, they should at least be fault-tolerant and fail-safe. Therefore, because of those requirements, "Formal Verification" can be usefull to obtain an assurance and guarantee of their correctness with respect to safety and security issues

Towards mechanized correctness proofs for cryptographic algorithms: Axiomatization of a probabilistic Hoare style logic

In [Corin, den Hartog in ICALP 2006] we build a formal verification technique for game based correctness proofs of cryptograhic algorithms based on a probabilistic Hoare style logic [den Hartog, de Vink in IJFCS 13(3), 2002]. An important step towards enabling mechanized verification within this technique is an axiomatization of implication between predicates which is purely semantically defined in [den Hartog, de Vink in IJFCS 13(3), 2002]. In this paper we provide an axiomatization and illustrate its place in the formal verification technique of [Corin, den Hartog in ICALP 2006]

rCOS: A refinement calculus for object systems

This article presents a mathematical characterization of object-oriented concepts by defining an observation-oriented semantics for a relational objectoriented language with a rich variety of features including subtypes, visibility, inheritance, type casting, dynamic binding and polymorphism. The language is expressive enough for the specification of object-oriented designs and programs. We also propose a calculus based on this model to support both structural and behavioral refinement of object-oriented designs. We take the approach of the development of the design calculus based on the standard predicate logic in Hoare and He’s Unifying Theories of Programming (UTP). We also consider object reference in terms of object identity as values and mutually dependent methods