Matthias Függer

Benedikt Bollig, Matthias Függer, Thomas Nowak

Multi-agent systems built on large language models (LLMs) are difficult to reason about. Coordination errors such as deadlocks or type-mismatched messages are often hard to detect through testing. We introduce a domain-specific language for specifying agent coordination based on message sequence charts (MSCs). The language separates message-passing structure from LLM actions, whose outputs remain unpredictable. We define the syntax and semantics of the language and present a syntax-directed projection that generates deadlock-free local agent programs from global coordination specifications. We illustrate the approach with a diagnosis consensus protocol and show how coordination properties can be established independently of LLM nondeterminism. We also describe a runtime planning extension in which an LLM dynamically generates a coordination workflow for which the same structural guarantees apply. An open-source Python implementation of our framework is available as ZipperGen.

Bernadette Charron-Bost, Matthias Függer, Thomas Nowak

We study the problem of asymptotic consensus as it occurs in a wide range of applications in both man-made and natural systems. In particular, we study systems with directed communication graphs that may change over time. We recently proposed a new family of convex combination algorithms in dimension one whose weights depend on the received values and not only on the communication topology. Here, we extend this approach to arbitrarily high dimensions by introducing two new algorithms: the ExtremePoint and the Centroid algorithm. Contrary to classical convex combination algorithms, both have component-wise contraction rates that are constant in the number of agents. Paired with a speed-up technique for convex combination algorithms, we get a convergence time linear in the number of agents, which is optimal. Besides their respective contraction rates, the two algorithms differ in the fact that the Centroid algorithm's update rule is independent of any coordinate system while the ExtremePoint algorithm implicitly assumes a common agreed-upon coordinate system among agents. The latter assumption may be realistic in some man-made multi-agent systems but is highly questionable in systems designed for the modelization of natural phenomena. Finally we prove that our new algorithms also achieve asymptotic consensus under very weak connectivity assumptions, provided that agent interactions are bidirectional.

Benedikt Bollig, Matthias Függer, Thomas Nowak et al.

We study model checking for an epistemic metric temporal logic with past, interpreted over finite Büchi automata under synchronous perfect recall. The logic is motivated by observation-based verification problems such as diagnosis and opacity, where an observer sees only a projection of an execution and reasons about events that may have occurred earlier. These requirements use no alternation between different agents' knowledge. We therefore consider the agent-alternation-free fragment, in which nested knowledge operators must refer to the same agent. We show that model checking for this fragment is EXPSPACE-complete. The lower bound already holds with one agent, one occurrence of the knowledge operator, and no non-trivial metric bounds. For the upper bound, we combine temporal test automata with perfect-recall observers. Because past formulas may have different truth values on indistinguishable histories ending in the same system state, the observer must track temporal automaton states in addition to system states.

Benedikt Bollig, Matthias Függer, Thomas Nowak et al.

We compare lightweight automata-based models (n-grams) with neural architectures (LSTM, Transformer) for next-activity prediction in streaming event logs. Experiments on synthetic patterns and five real-world process mining datasets show that n-grams with appropriate context windows achieve comparable accuracy to neural models while requiring substantially fewer resources. Unlike windowed neural architectures, which show unstable performance patterns, n-grams provide stable and consistent accuracy. While we demonstrate that classical ensemble methods like voting improve n-gram performance, they require running many agents in parallel during inference, increasing memory consumption and latency. We propose an ensemble method, the promotion algorithm, that dynamically selects between two active models during inference, reducing overhead compared to classical voting schemes. On real-world datasets, these ensembles match or exceed the accuracy of non-windowed neural models with lower computational cost.

Victoria Andaur, Janna Burman, Matthias Függer et al.

We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct competition among microbial species influences their ability to reach majority consensus. In this problem, two species are designated as input species, and the goal is to guarantee that eventually only the input species which had the highest initial count prevails. We show that direct competition dynamics reach majority consensus with high probability even when the initial gap between the species is small, i.e., $Ω(\sqrt{n\log n})$, where $n$ is the initial population size. In contrast, we show that absence of direct competition is not robust: solving majority consensus with constant probability requires a large initial gap of $Ω(n)$. To corroborate our analytical results, we use simulations to show that these consensus dynamics occur within practical biological time scales.

Benedikt Bollig, Matthias Függer, Thomas Nowak

We present a Python-based framework for event-log prediction in streaming mode, enabling predictions while data is being generated by a business process. The framework allows for easy integration of streaming algorithms, including language models like n-grams and LSTMs, and for combining these predictors using ensemble methods. Using our framework, we conducted experiments on various well-known process-mining data sets and compared classical batch with streaming mode. Though, in batch mode, LSTMs generally achieve the best performance, there is often an n-gram whose accuracy comes very close. Combining basic models in ensemble methods can even outperform LSTMs. The value of basic models with respect to LSTMs becomes even more apparent in streaming mode, where LSTMs generally lack accuracy in the early stages of a prediction run, while basic methods make sensible predictions immediately.

Zhuofan Xu, Benedikt Bollig, Matthias Függer et al.

The Centralized Training with Decentralized Execution (CTDE) paradigm has gained significant attention in multi-agent reinforcement learning (MARL) and is the foundation of many recent algorithms. However, decentralized policies operate under partial observability and often yield suboptimal performance compared to centralized policies, while fully centralized approaches typically face scalability challenges as the number of agents increases. We propose Centralized Permutation Equivariant (CPE) learning, a centralized training and execution framework that employs a fully centralized policy to overcome these limitations. Our approach leverages a novel permutation equivariant architecture, Global-Local Permutation Equivariant (GLPE) networks, that is lightweight, scalable, and easy to implement. Experiments show that CPE integrates seamlessly with both value decomposition and actor-critic methods, substantially improving the performance of standard CTDE algorithms across cooperative benchmarks including MPE, SMAC, and RWARE, and matching the performance of state-of-the-art RWARE implementations.

Bernadette Charron-Bost, Matthias Függer, Thomas Nowak

In this note, we give a complete proof that Hegselmann-Krause systems converge on the circle following the proof strategy developed by Hegarty, Martinsson, and Wedin.