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The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for…

Programs with multiphase control-flow are programs where the execution passes through several (possibly implicit) phases. Proving termination of such programs (or inferring corresponding runtime bounds) is often challenging since it…

Bounded model checking (BMC) is vital for finding program property violations. For unsafe programs, BMC can quickly find an execution path from an initial state to the violated state that refutes a given safety property. However, BMC…

Backtracking (i.e., reverse execution) helps the user of a debugger to naturally think backwards along the execution path of a program, and thinking backwards makes it easy to locate the origin of a bug. So far backtracking has been…

Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…

We introduce a method of verifying termination of logic programs with respect to concrete queries (instead of abstract query patterns). A necessary and sufficient condition is established and an algorithm for automatic verification is…

Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…

We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…

For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is…

In previous work, we presented a symbolic execution method which starts with a concrete model of the program but progressively abstracts away details only when these are known to be irrelevant using interpolation. In this paper, we extend…

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…

Runtime verification is a lightweight verification technique that complements model checking by analyzing system executions at runtime rather than exploring a complete system model in advance. It is particularly useful for partially…

Reasoning models produce long traces of intermediate decisions and tool calls, making test-time verification important for ensuring correctness. Existing approaches either verify only the final answer, which misses early errors, or rely on…

The complexity of software in embedded systems has increased significantly over the last years so that software verification now plays an important role in ensuring the overall product quality. In this context, SAT-based bounded model…

We present an approach for verifying systems at runtime. Our approach targets distributed systems whose components communicate with monitors over unreliable channels, where messages can be delayed, reordered, or even lost. Furthermore, our…

The aim is to create reliable and verifiable fault detection software to detect abrupt changes in safety-critical dynamic systems. Fault detection methods are implemented as software on digital computers that monitor and control the system.…

Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs. To this end, a variety of acceleration techniques has been proposed. However, so far all of them have been monolithic, i.e., a…

Modern model checking techniques concentrate on global properties of verified systems, because the methods base on global state space. Local features like partial deadlock or process termination are not easy to express and check. In the…

The integration of Formal Verification tools with Large Language Models (LLMs) offers a path to scale software verification beyond manual workflows. However, current methods remain unreliable: without a solid theoretical footing, the…

We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…