Program Analysis in A Combined Abstract Domain

Automated verification of heap-manipulating programs is a challenging task due to the complexity of aliasing and mutability of data structures used in these programs. The properties of a number of important data structures do not only relate to one domain, but to combined multiple domains, such as sorted list, priority queues, height-balanced trees and so on. The safety and sometimes efficiency of programs do rely on the properties of those data structures. This thesis focuses on developing a verification system for both functional correctness and memory safety of such programs which involve heap-based data structures. Two automated inference mechanisms are presented for heap-manipulating programs in this thesis. Firstly, an abstract interpretation based approach is proposed to synthesise program invariants in a combined pure and shape domain. Newly designed abstraction, join and widening operators have been defined for the combined domain. Furthermore, a compositional analysis approach is described to discover both pre-/post-conditions of programs with a bi-abduction technique in the combined domain. As results of my thesis, both inference approaches have been implemented and the obtained results validate the feasibility and precision of proposed approaches. The outcomes of the thesis confirm that it is possible and practical to analyse heap-manipulating programs automatically and precisely by using abstract interpretation in a sophisticated combined domain

Actor Network Procedures as Psi-calculi for Security Ceremonies

The actor network procedures of Pavlovic and Meadows are a recent graphical formalism developed for describing security ceremonies and for reasoning about their security properties. The present work studies the relations of the actor network procedures (ANP) to the recent psi-calculi framework. Psi-calculi is a parametric formalism where calculi like spi- or applied-pi are found as instances. Psi-calculi are operational and largely non-graphical, but have strong foundation based on the theory of nominal sets and process algebras. One purpose of the present work is to give a semantics to ANP through psi-calculi. Another aim was to give a graphical language for a psi-calculus instance for security ceremonies. At the same time, this work provides more insight into the details of the ANPs formalization and the graphical representation.Comment: In Proceedings GraMSec 2014, arXiv:1404.163

Verification and falsification of programs with loops using predicate abstraction

Predicate abstraction is a major abstraction technique for the verification of software. Data is abstracted by means of Boolean variables, which keep track of predicates over the data. In many cases, predicate abstraction suffers from the need for at least one predicate for each iteration of a loop construct in the program. We propose to extract looping counterexamples from the abstract model, and to parametrise the simulation instance in the number of loop iterations. We present a novel technique that speeds up the detection of long counterexamples as well as the verification of programs with loop

Staged Specifications for Automated Verification of Higher-Order Imperative Programs

Higher-order functions and imperative references are language features supported by many mainstream languages. Their combination enables the ability to package references to code blocks with the captured state from their environment. Higher-order imperative programs are expressive and useful, but complicate formal specification and reasoning due to the use of yet-to-be-instantiated function parameters, especially when their invocations may mutate memory captured by or reachable from their arguments. Existing state-of-the-art works for verifying higher-order imperative behaviors are restricted in two ways: achieving strong theoretical results without automated implementations, or achieving automation with the help of strong assumptions from dedicated type systems (e.g. Rust). To enable an automated verification solution for imperative languages without the above restrictions, we introduce Higher-order Staged Separation Logic (HSSL), an extension of Hoare logic for call-by-value higher-order functions with ML-like local references. In this paper, we design a novel staged specification logic, prove its soundness, develop a new automated higher-order verifier, Heifer, for a core OCaml-like language, report on experimental results, and present various case studies investigating its capabilities

Automating Program Verification and Repair Using Invariant Analysis and Test Input Generation

Software bugs are a persistent feature of daily life---crashing web browsers, allowing cyberattacks, and distorting the results of scientific computations. One approach to improving software uses program invariants---mathematical descriptions of program behaviors---to verify code and detect bugs. Current invariant generation techniques lack support for complex yet important forms of invariants, such as general polynomial relations and properties of arrays. As a result, we lack the ability to conduct precise analysis of programs that use this common data structure. This dissertation presents DIG, a static and dynamic analysis framework for discovering several useful classes of program invariants, including (i) nonlinear polynomial relations, which are fundamental to many scientific applications; disjunctive invariants, (ii) which express branching behaviors in programs; and (iii) properties about multidimensional arrays, which appear in many practical applications. We describe theoretical and empirical results showing that DIG can efficiently and accurately find many important invariants in real-world uses, e.g., polynomial properties in numerical algorithms and array relations in a full AES encryption implementation. Automatic program verification and synthesis are long-standing problems in computer science. However, there has been a lot of work on program verification and less so on program synthesis. Consequently, important synthesis tasks, e.g., generating program repairs, remain difficult and time-consuming. This dissertation proves that certain formulations of verification and synthesis are equivalent, allowing for direct applications of techniques and tools between these two research areas. Based on these ideas, we develop CETI, a tool that leverages existing verification techniques and tools for automatic program repair. Experimental results show that CETI can have higher success rates than many other standard program repair methods

Verification of Pointer-Based Programs with Partial Information

The proliferation of software across all aspects of people's life means that software failure can bring catastrophic result. It is therefore highly desirable to be able to develop software that is verified to meet its expected specification. This has also been identified as a key objective in one of the UK Grand Challenges (GC6) (Jones et al., 2006; Woodcock, 2006). However, many difficult problems still remain in achieving this objective, partially due to the wide use of (recursive) shared mutable data structures which are hard to keep track of statically in a precise and concise way. This thesis aims at building a verification system for both memory safety and functional correctness of programs manipulating pointer-based data structures, which can deal with two scenarios where only partial information about the program is available. For instance the verifier may be supplied with only partial program specification, or with full specification but only part of the program code. For the first scenario, previous state-of-the-art works (Nguyen et al., 2007; Chin et al., 2007; Nguyen and Chin, 2008; Chin et al, 2010) generally require users to provide full specifications for each method of the program to be verified. Their approach seeks much intellectual effort from users, and meanwhile users are liable to make mistakes in writing such specifications. This thesis proposes a new approach to program verification that allows users to provide only partial specification to methods. Our approach will then refine the given annotation into a more complete specification by discovering missing constraints. The discovered constraints may involve both numerical and multiset properties that could be later confirmed or revised by users. Meanwhile, we further augment our approach by requiring only partial specification to be given for primary methods of a program. Specifications for loops and auxiliary methods can then be systematically discovered by our augmented mechanism, with the help of information propagated from the primary methods. This work is aimed at verifying beyond shape properties, with the eventual goal of analysing both memory safety and functional properties for pointer-based data structures. Initial experiments have confirmed that we can automatically refine partial specifications with non-trivial constraints, thus making it easier for users to handle specifications with richer properties. For the second scenario, many programs contain invocations to unknown components and hence only part of the program code is available to the verifier. As previous works generally require the whole of program code be present, we target at the verification of memory safety and functional correctness of programs manipulating pointer-based data structures, where the program code is only partially available due to invocations to unknown components. Provided with a Hoare-style specification ({Pre} prog {Post}) where program (prog) contains calls to some unknown procedure (unknown), we infer a specification (mspecu) for the unknown part (unknown) from the calling contexts, such that the problem of verifying program (prog) can be safely reduced to the problem of proving that the unknown procedure (unknown) (once its code is available) meets the derived specification (mspecu). The expected specification (mspecu) is automatically calculated using an abduction-based shape analysis specifically designed for a combined abstract domain. We have implemented a system to validate the viability of our approach, with encouraging experimental results