Max Planck Institute for Software Systems

Dynamic Bayesian networks (DBNs) are compact graphical representations used to model probabilistic systems where interdependent random variables and their distributions evolve over time. In this paper, we study the verification of the evolution of conditional-independence (CI) propositions against temporal logic specifications. To this end, we consider two specification formalisms over CI propositions: linear temporal logic (LTL), and non-deterministic Büchi automata (NBAs). This problem has two variants. Stochastic CI properties take the given concrete probability distributions into account, while structural CI properties are viewed purely in terms of the graphical structure of the DBN. We show that deciding whether a stochastic CI proposition eventually holds is at least as hard as the Skolem problem for linear recurrence sequences, which is a long-standing open problem in number theory. On the other hand, we show that verifying the evolution of structural CI propositions against LTL and NBA specifications is in PSPACE, and is hard for both NP and coNP. We also identify natural restrictions on the graphical structure of the DBN that make the verification of structural CI properties tractable.

Ensuring the safety of AI-enabled systems, particularly in high-stakes domains such as autonomous driving and healthcare, has become increasingly critical. Traditional formal verification tools fall short when faced with systems that embed both opaque, black-box AI components and complex stochastic dynamics. To address these challenges, we introduce LUCID (Learning-enabled Uncertainty-aware Certification of stochastIc Dynamical systems), a verification engine for certifying safety of black-box stochastic dynamical systems from a finite dataset of random state transitions. As such, LUCID is the first known tool capable of establishing quantified safety guarantees for such systems. Thanks to its modular architecture and extensive documentation, LUCID is designed for easy extensibility. LUCID employs a data-driven methodology rooted in control barrier certificates, which are learned directly from system transition data, to ensure formal safety guarantees. We use conditional mean embeddings to embed data into a Reproducing Kernel Hilbert Space (RKHS), where an RKHS ambiguity set is constructed that can be inflated to robustify the result to out-of-distribution behavior. A key innovation within LUCID is its use of a finite Fourier kernel expansion to reformulate a semi-infinite non-convex optimization problem into a tractable linear program. The resulting spectral barrier allows us to leverage the fast Fourier transform to generate the relaxed problem efficiently, offering a scalable yet distributionally robust framework for verifying safety. LUCID thus offers a robust and efficient verification framework, able to handle the complexities of modern black-box systems while providing formal guarantees of safety. These unique capabilities are demonstrated on challenging benchmarks.

Recent advances in reinforcement learning (RL) have renewed focus on the design of reward functions that shape agent behavior. Manually crafting such functions is often tedious and error-prone. A more principled alternative is to specify behavioral requirements using a formal, unambiguous language that can be automatically translated into a reward function. Omega-regular languages are a natural choice for this purpose, given their established role in formal verification and synthesis. However, existing approaches using omega-regular specifications typically rely on discounted reward RL in an episodic setting, where the environment is periodically reset to an initial state during learning. This setup is misaligned with the semantics of omega-regular specifications, which describe properties over infinite behavior traces. In such cases, the average reward criterion and the continuing setting—where the agent interacts with the environment over a single, uninterrupted lifetime—are more appropriate. To address the challenges of infinite-horizon, continuing tasks, we restrict our focus to the subclass of omega-regular languages known as absolute liveness specifications. These specifications cannot be violated by any finite prefix of the agent’s behavior, aligning naturally with the continuing setting. We present the first model-free RL framework that translates absolute liveness specifications to average-reward objectives. In contrast to prior work, our approach enables learning in communicating Markov Decision Processes without episodic resetting. We further introduce a reward structure for lexicographic multi-objective optimization, where the goal is to maximize an external average-reward objective among the policies that also maximize the satisfaction probability of a given absolute liveness omega-regular specification. Our method guarantees convergence in unknown communicating MDPs and supports on-the-fly reductions that do not require full knowledge of the environment, thus enabling model-free RL. Empirical results across various benchmarks demonstrate that our average-reward approach in the continuing setting is more effective than competing methods based on discounting.

Recent advances in automated programming have the potential to reduce human involvement in the software engineering process, but this can lead to less trustworthy software. We envision a three-pronged approach to automating the engineering of trustworthy software that involves (1) eliciting requirements from users and automatically generating formal specifications encoding users’ intent, (2) automatically synthesizing source code conforming to those specifications, and (3) automatically synthesizing formal proofs to verify the correctness of the produced software. We describe this vision and the state of the art in each of these three areas, and the research challenges that must be overcome in each area and in their integration.

This editorial introduces the first part of the Special Issue on “Advanced Technologies in the Decentralized Web.” As the Internet evolves toward more user-centric and resilient architectures, concepts like Web3 and Web 3.0 have gained significant prominence. This issue explores key advancements including decentralized machine learning, AI-blockchain integration, identity management, and data sovereignty. We provide an overview of the selected papers, highlighting their contributions to creating a more transparent and secure decentralized digital future.

The reachability problem in multi-pushdown automata (MPDA), or equivalently, interleaved Dyck reachability, has many applications in static analysis of recursive programs. An example is safety verification of multi-threaded recursive programs with shared memory. Since these problems are undecidable, the literature contains many decidable (and efficient) underapproximations of MPDA. A uniform framework that captures many of these underapproximations is that of bounded treewidth : To each execution of the MPDA, we associate a graph; then we consider the subset of all graphs that have a treewidth at most k , for some constant k . In fact, bounding treewidth is a generic approach to obtain classes of systems with decidable reachability, even beyond MPDA underapproximations. The resulting systems are also called MSO-definable bounded-treewidth systems . While bounded treewidth is a powerful tool for reachability and similar types of analysis, the word languages (i.e. action sequences corresponding to executions) of these systems remain far from understood. For the slight restriction of bounded special treewidth , or “bounded-stw” (which is equivalent to bounded treewidth on MPDA, and even includes all bounded-treewidth systems studied in the literature), this work reveals a connection with multiple context-free languages (MCFL), a concept from computational linguistics. We show that the word languages of MSO-definable bounded-stw systems are exactly the MCFL. We exploit this connection to provide an optimal algorithm for computing downward closures for MSO-definable bounded-stw systems. Computing downward closures is a notoriously difficult task that has many applications in the verification of complex systems: As an example application, we show that in programs with dynamic spawning of MSO-definable bounded-stw processes, safety verification has the same complexity as in the case of processes with sequential recursive processes.

Remote Direct Memory Access (RDMA) is a memory technology that allows remote devices to directly write to and read from each other's memory, bypassing components such as the CPU and operating system. This enables low-latency high-throughput networking, as required for many modern data centres, HPC applications and AI/ML workloads. However, baseline RDMA comprises a highly permissive weak memory model that is difficult to use in practice and has only recently been formalised. In this paper, we introduce the Library of Composable Objects (LOCO), a formally verified library for building multi-node objects on RDMA, filling the gap between shared memory and distributed system programming. LOCO objects are well-encapsulated and take advantage of the strong locality and the weak consistency characteristics of RDMA. They have performance comparable to custom RDMA systems (e.g. distributed maps), but with a far simpler programming model amenable to formal proofs of correctness. To support verification, we develop a novel modular declarative verification framework, called Mowgli, that is flexible enough to model multinode objects and is independent of a memory consistency model. We instantiate Mowgli with the RDMA memory model, and use it to verify correctness of LOCO libraries.

Bacterial antimicrobial resistance is one of the most pressing global health challenges. Infections with resistant pathogens increase patient morbidity and mortality due to limited treatment options. Rapid and reliable identification of resistance is therefore crucial. However, conventional culture-based diagnostics are slow, typically requiring at least 48 hours from patient sample arrival to result. In contrast, matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry, routinely used for species identification, can provide data 24 hours earlier. Repurposing this technique for antimicrobial resistance prediction has shown promise, but limited predictive performance and a lack of statistically grounded uncertainty estimates have hindered clinical integration. To address these issues, we propose an antimicrobial resistance detection framework using a knowledge-graph-enhanced conformal predictor. Conformal prediction outputs sets of likely effective antibiotics with statistical guarantees, ensuring that resistance detection meets a predefined error rate. Our approach improves upon standard conformal prediction by integrating domain knowledge through a drug- and species-specific knowledge graph that captures interdependencies between antibiotics, such as inferable resistance patterns between broad- and narrow-spectrum agents, as well as co-resistance patterns within antibiotic classes. This predictor is layered on top of a novel classifier that surpasses state-of-the-art models and overcomes key technical limitations of earlier approaches. We evaluated our framework on two clinically relevant species, Klebsiella pneumoniae and Escherichia coli, using the DRIAMS dataset. Our results demonstrate that our conformal predictor consistently achieved the expected coverage guarantees and that the knowledge-graph enhancement significantly reduced false discovery rates compared to standard conformal approaches. By adding statistically grounded uncertainty estimates and improving predictive performance, our framework strengthens the reliability of early antimicrobial resistance predictions from MALDI-TOF data. This could support the clinical integration of such rapid diagnostics by increasing trust in their results and enabling better-informed early treatment decisions.1.

Abstract Let p and q be two distinct fixed prime numbers and $$(n_i)_{i\ge 0}$$ the sequence of consecutive integers of the form $$p^a\cdot q^b$$ with $$a,b\ge 0$$ . Tijdeman gave a lower bound (1973) and an upper bound (1974) for the gap size $$n_{i+1}-n_i$$ , with each bound containing an unspecified exponent and implicit constant. We will explicitly bound these four quantities. Earlier Langevin (1976) gave weaker estimates for (only) the exponents. Given a real number $$\alpha >1$$ , there exists a smallest number m such that for every $$n\ge m$$ , there exists an integer $$n_i$$ in $$[n,n\alpha )$$ . Our effective version of Tijdeman’s result immediately implies an upper bound for m , which using the Koksma–Erdős–Turan inequality we will improve on. We present a fast algorithm to determine m when $$\max \{p,q\}$$ is not too large and demonstrate it with numerical material. In an appendix we explain, given $$n_i$$ , how to efficiently determine both $$n_{i-1}$$ and $$n_{i+1}$$ , something closely related to work of Bérczes, Dujella and Hajdu.