by Sjaak Smetsers and Marko van Eekelen

Due to its great complexity, it is inevitable that modern software will suffer from the presence of numerous errors. These software bugs are frequent sources of security vulnerabilities, and in safety-critical systems, they are not simply expensive annoyances: they can endanger lives. The growing demand for high availability and reliability of computer systems has led to a formal verification of such systems.

There are two principal approaches to formal verification: model checking and theorem proving.


There are two principal approaches to formal verification: model checking and theorem proving.

The goal of this project is to develop a methodology for improving the quality of software by combining model checking with theorem proving such that the advantages of both methods are fully exploited. Additionally, we enhance existing or develop new techniques to support the various translations of conversions that are needed in this process.

The proposed methodology resembles what in software engineering is called code refactoring. However, the latter replaces existing code with the same functionality. It does not fix bugs; rather it improves the understandability of the code by changing its internal structure.

The proposed methodology consists of the following steps:

  • the software system is analysed to identify and localize 'suspicious' parts
  • a formal model of these parts is created
  • the model is verified by the model checker and, if necessary, improved until it is approved by the checker
  • for full reliability the model is converted into a PVS specification. PVS (Prototype Verification System) is a proof tool providing a theorem specification language and support for developing correctness proofs. This tool is used to construct a full formal proof of the system
  • from this PVS specification new code is derived that replaces the original (possibly erroneous) code. In this way one obtains highly reliable code, since it corresponds directly to a fully proven formal model.
Figure 1: The LaQuSo FM based approach.
Figure 1: The LaQuSo FM based approach.

These steps are illustrated in Figure 1. We will briefly discuss each of them.

  • Identification. Most of the time, the software system will be too large to be handled completely. Instead one must first identify the safety-critical or erroneous parts. The process of determining the parts of a program relevant to the property to be checked is often called slicing.
  • Abstraction. There exist several techniques by which formal models can be obtained from source code. Due to the state explosion problem, a direct instruction-wise translation of source code is unsuitable. The methods for alleviating this problem can be divided into two categories: abstraction and symbolic evaluation. With abstraction, the state space is reduced by employing specific knowledge about the system in order to model only the relevant features. In the symbolic evaluation approach, the abstraction occurs at the level of the model itself. Using succinct data structures and symbolic algorithms, state information can be compressed, thus helping to keep state explosion under control.
  • Conversion. At present, no tool exists to convert a model into a PVS specification. This is future work.
  • Code generation. From the PVS specification, code will be generated that can replace the original (possibly faulty) code. Most theorem provers (Isabelle, Coq, PVS) are already equipped with code generators, which have in common that they produce functional code. We are currently developing a generator capable of generating code for imperative languages like Java. An interesting aspect is the extension of Java code with proof information leading to so-called proof-carrying code.

The figure has two feedback steps:

  • Counterexample. If the attempt to check the abstract model fails, there is a counterexample which can be used directly to adjust the source code, provided that the counterexample was genuine. If the latter is not the case, our abstract model is probably too coarse and must be refined further. A technique is developed which iteratively uses spurious counter¬examples to create an abstract model with the right level of abstraction.
  • Validation. The theorem-proving process is very sensitive to the way in which properties are formulated. In the case of state transition systems, this boils down to the right formulation of invariants. The problem with these invariants is that they are usually very subtle and therefore very difficult to specify. One may easily overlook a detail, thus making the invariant invalid. Instead of immediately checking invariants in the theorem prover itself, we propose using the model checker to quickly trace and repair flaws before we start proving the invariants. This step requires a translation of PVS properties to equivalent statements in the language of the model checker. As far we know, this has not been done before.

We apply our methodology in the context of the Laboratory for Quality Software (LaQuSo), which is a joint activity between the Technical University Eindhoven and the Radboud University Nijmegen. Within LaQuSo, successful case studies have been performed for safety-critical software components. In the near future we expect to apply our approach to cases such as control software for the Dutch 'Maeslantkering' water barrier and to programmable hardware to replace traditional components in nuclear plants

Related publications:

Please contact:
Marko van Eekelen
Radboud University Nijmegen, The Netherlands
Tel: +31 24 365 3410

Next issue: January 2023
Special theme:
"Cognitive AI & Cobots"
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