Program Verification (Lecture)

Motivation

Contents

Although we will use tools this is a rather theoretical lecture in which we will learn the basic concepts of program verification.

We will often reduce problems to the satisfiability problem of logical formulas. (So if you do not like mathematical logic, you probably do not want to take this lecture.) E.g, a satisfying assignment for the following formula will show us how the assert statement in the depicted program can be violated.

  x_0 >= 0 /\ y_0 >=0 /\ x_0<=4294967296 /\ y_0<=4294967296 /\ x_0 + y_0 <= 42 /\ y_0 >= 100 /\ x_1 = (2*x_0-y_0)%4294967296 /\ x+y < 100

void foo(unsigned int x, unsigned int y) {
    while (x+y <=42) {
        if (y >= 100) {
            x = 2 * x - y;
            //@ assert (x+y >= 100);
        }
        y++
    }
}

In order to get familiar with logical reasoning, the course will start with an introduction to propositional logic and first-order logic. We will then formally introduce the Hoare calculus which will allow us to state the correctness of a program and to give a mathematical proof that the program is correct.

Throughout this lecture, we will use tool like the Z3 SMT solver or the Ultimate Automizer software verifier in order to see the effect of our algorithms on practical examples. E.g., if we want to find out if the following C program is correct, we can ask Ultimate Automizer.

int main() {
    unsigned char pos = getInitialPosition();
    int arr[256];
    while(1) {
        arr[pos] = getNextValue();
        arr[pos + 1] = getNextValue();
        pos += 2;
    }
    return 0;
}

E-Learning

The course will be organized online in the Ilias system.The main course material are slides, exercises, and videos. Additionally we will have interactive sessions via BigBlueButton, which is itegrated in Ilias. The interactive sessions are NOT recorded.

The slide set consists of three kinds of slides. First, there are slides that I would show in a presentation. Some of these slides are accompanied by additional slides (the slides with violet text) that contain the information that I would say while giving the presentation. Furthermore there are slides that look like titlepages, have blue background and tell you the range of slides that is discussed in the next virtual classroom.

The slides are very similar to a lecture script and the idea is that you read the slides before the next interactive sessions. Your efforts to understand the slides will be supported by exercises that you hand in before the next interactive sessions. In the interactive sessions we will go very quickly through the slides and discuss only your questions. Furthermore, we will discuss your solutions for the exercises. For some topics, e.g., presentation of tools, carrying out difficult algorithms, motivating a new concept, we will record videos.

We are very happy to improve the course material. If you have questions and you think something should be explained in more detail then please let us know.

Slides

The lecture slides are the main course material. Starting from Section 2 the slides are annotated with additional information and can be seen as a kind of lecture script.

The slides will be updated frequently. We will not only append new content but depending on the questions in interactive sessions we will also insert slides with additional information.

Videos

Exercises

Exam

There will be an exam during the examination period. Prerequisite for admission to the exam is an active participation in the exercises. A sufficient criterion for an active participation in the exercises is that you achieved 50% of the points that can be obtained for exercise sheets and presented an exercise in an interactive session.

Literature

• Almeida, J.B., Frade, M.J., Pinto, J.S., Melo de Sousa, S., Rigorous Software Development - An Introduction to Program Verification, Springer 2011, ISBN 978-0-85729-017-5
• Matthias Heizmann, Jochen Hoenicke, Andreas Podelski: Software Model Checking for People Who Love Automata. CAV 2013

• Traces, interpolants, and automata : Ultimate Automizer’s approach to software verification
  Talk given at the EPIT Spring School 2018