Tight polynomial worst-case bounds for loop programs

In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to decide precisely whether a program has certain growth-rate properties, in particular whether a computed value, or the program's running time, has a polynomial growth rate. A natural and intriguing problem was to move from answering the decision problem to giving a quantitative result, namely, a tight polynomial upper bound. This paper shows how to obtain asymptotically-tight, multivariate, disjunctive polynomial bounds for this class of programs. This is a complete solution: whenever a polynomial bound exists it will be found. A pleasant surprise is that the algorithm is quite simple; but it relies on some subtle reasoning. An important ingredient in the proof is the forest factorization theorem, a strong structural result on homomorphisms into a finite monoid

Abstractions and Static Analysis for Verifying Reactive Systems

Fokkink, W.J. [Promotor]Sidorova, N. [Copromotor

Context Aware Model-Checking for Embedded Software

Reactive systems are becoming extremely complex with the huge increase in high technologies. Despite technical improvements, the increasing size of the systems makes the introduction of a wide range of potential errors easier. Among reactive systems, the asynchronous systems communicating by exchanging messages via buffer queues are often characterized by a vast number of possible behaviors. To cope with this difficulty, manufacturers of industrial systems make significant efforts in testing and simulation to successfully pass the certification process. Nevertheless revealing errors and bugs in this huge number of behaviors remains a very difficult activity. An alternative method is to adopt formal methods, and to use exhaustive and automatic verification tools such as model-checkers. Model-checking algorithms can be used to verify requirements of a model formally and automatically. Several model checkers as (Berthomieu et al., 2004; Holzmann, 1997; Larsen et al., 1997), have been developed to help the verification of concurrent asynchronous systems. It is well known that an important issue that limits the application of model checking techniques in industrial software projects is the combinatorial explosion problem (Clarke et al., 1986; Holzmann & Peled, 1994; Park & Kwon, 2006). Because of the internal complexity of developed software, model checking of requirements over the system behavioral models could lead to an unmanageable state space. The approach described in this chapter presents an exploratory work to provide solutions to the problems mentioned above. It is based on two joint ideas: first, to reduce behaviors system to be validated during model-checking and secondly, help the user to specify the formal properties to check. For this, we propose to specify the behavior of the entities that compose the system environment. These entities interact with the system. Their behaviors are described by use cases (scenarios) called here contexts. They describe how the environment interacts with the system. Each context corresponds to an operational phase identified as system initialization, reconfiguration, graceful degradation, etc.. In addition, each context is associated with a set of properties to check. The aim is to guide the model-checker to focus on a restriction of the system behavior for verification of specific properties instead on exploring the global system automaton

Message sequence chart specifications with cross verification

Current software specification verification methods are usually performed within the context of the specification method. There is little cross verification, pitting one type of specification against another, taking place. The most common techniques involve syntax checks across specifications or doing specification transformations and running verification within the new context. Since viewpoints of a system are different even within programming teams we concentrate on producing an efficient way to run cross verification on specifications, particularly specifications written with Message Sequence Charts and State Transition Diagrams.;In this work an algorithm is proposed in which all conditional MSCs are transformed into an algebraic representations, Message Flow Graphs and by stepwise refinement, a Global State Transition Graph is created. This GSTG has all the properties of a State Transition Diagram and therefore can be analyzed in conjunction with the original STD

Modeling and formal verification of gaming storylines

Video games are becoming more and more interactive with increasingly complex plots. These plots typically involve multiple parallel storylines that may converge and diverge based on player actions. This may lead to situations that are inconsistent or impassable. Current techniques for planning and testing game plots involve naive means such as text documents, spreadsheets, and critical path testing. Recent academic research [1] [2] [3] examines the design planning problems, but neglect testing and verification of the possible plot lines. These complex plots have thus until now been handled inadequately due to a lack of a formal methodology and tools to support them. In this dissertation, we describe how we develop methods to 1) characterize storylines (SChar), 2) define a storyline description language (SDL), and 3) create a storyline verification tool based in formal verification techniques (StoCk) that use our SDL as input. SChar (Storyline Characterization) help game developers characterize the category of story line they are working on (e.g. linear, branching and plot) through a tool that give a set of guided questions. Our SDL allows its users to describe storylines in a consistent format similar to how they reason about storylines, but in such a way that it can be used for formal verification. StoCk accepts storylines, described in SDL, to be formally verified using SPIN for errors. StoCk is also examined in three common use cases found in the gaming industry used as a tool 1) during storyline creation 2) during quality assurance and 3) during storyline implementation. The combination of SChar, SDL, and StoCk provides designers, writers, and developers a novel methodology and tools to verify consistency in large and complex game plots.Electrical and Computer Engineerin

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