Combining Abstract Domains for Software Model Checking

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Hajdu Ákos
Department of Measurement and Information Systems

Software systems are controlling devices that surround us in our everyday life. Many of these systems are safety-critical (e.g., autonomous vehicles, power plants), thus ensuring their correct operation is gaining increasing importance. Formal verification techniques can both reveal errors and give guarantees on correctness with a sound mathematical basis. One of the most widely used formal verification approaches is model checking, which systematically examines all possible states and transitions (i.e., the state space) of the software. However, a major drawback of model checking is its high computational complexity, often preventing its application on real-life software.

Counterexample-guided abstraction refinement (CEGAR) is a supplementary technique, making model checking more efficient in practice. CEGAR works by iteratively constructing and refining abstractions in a given abstract domain. There are several existing domains, such as explicit-values, which only track a relevant subset of program variables and predicates, which use logical formulas instead of concrete values. Observations show that different abstract domains are more suitable for different kinds of software systems. Therefore, so-called product domains have also emerged that combine different domains into a single algorithm.

In this work, we develop and examine various strategies to combine the explicit-value domain with predicates. Our approaches use different information from the already explored abstract state space to guide further exploration more efficiently. We implement our new strategies on top of Theta, an open source verification framework. This allows us to perform an experiment with a wide range of software systems including industrial PLC codes. We evaluate the strengths and weaknesses of the different approaches and we also compare them to existing methods. Our experiments show that the new strategies can form efficient combinations of the existing algorithms.


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