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Anne-Kathrin Schmuck

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Published work

8 published item(s)

preprint2026arXiv

MANTRA: Synthesizing SMT-Validated Compliance Benchmarks for Tool-Using LLM Agents

Tool-using large language model (LLM) agents are increasingly deployed in settings where their reliable behavior is governed by strict procedural manuals. Ensuring that such agents comply with the rules from these manuals is challenging, as they are typically written for humans in natural language while agent behavior manifests as an execution trace of tool calls. Existing evaluations of LLM agents rely on manually constructed benchmarks or LLM-based judges, which either do not scale or lack reliability for complex, long-horizon manuals. To overcome these limitations, we present MANTRA, a framework for automatically synthesizing machine-checkable compliance benchmarks from natural-language manuals and tool schemas. MANTRA independently generates (i) a symbolic world model capturing procedural dependencies, and (ii) a set of trace-level compliance checks for a given task, and validates their consistency using SMT solving. A structured repair loop resolves inconsistencies, requiring human intervention only as a fallback. %This yields benchmarks that are formally validated. Importantly, MANTRA supports arbitrary domains and long procedural manuals, and provides a tunable notion of task complexity which is utilized to automatically derive challenging tasks accompanying compliance checks. Using MANTRA, we build a new benchmark suite with 285 tasks across 6 domains scaling to 50+ page manuals with minimal human effort. Empirically, we show that the compliance checks are richer with stronger constraint enforcement compared to existing benchmarks. Additionally, the granularity of the checks can be used for debugging the agents' failure modes. These results demonstrate that combining automated benchmark generation with formally grounded validation methods enables scalable and reliable benchmarking of tool-using agents.

preprint2020arXiv

On Abstraction-Based Controller Design With Output Feedback

We consider abstraction-based design of output-feedback controllers for dynamical systems with a finite set of inputs and outputs against specifications in linear-time temporal logic. The usual procedure for abstraction-based controller design (ABCD) first constructs a finite-state abstraction of the underlying dynamical system, and second, uses reactive synthesis techniques to compute an abstract state-feedback controller on the abstraction. In this context, our contribution is two-fold: (I) we define a suitable relation between the original system and its abstraction which characterizes the soundness and completeness conditions for an abstract state-feedback controller to be refined to a concrete output-feedback controller for the original system, and (II) we provide an algorithm to compute a sound finite-state abstraction fulfilling this relation. Our relation generalizes feedback-refinement relations from ABCD with state-feedback. Our algorithm for constructing sound finite-state abstractions is inspired by the simultaneous reachability and bisimulation minimization algorithm of Lee and Yannakakis. We lift their idea to the computation of an observation-equivalent system and show how sound abstractions can be obtained by stopping this algorithm at any point. Additionally, our new algorithm produces a realization of the topological closure of the input/output behavior of the original system if it is finite-state realizable.

preprint2020arXiv

Resilient Abstraction-Based Controller Design

We consider the computation of resilient controllers for perturbed non-linear dynamical systems w.r.t. linear-time temporal logic specifications. We address this problem through the paradigm of Abstraction-Based Controller Design (ABCD) where a finite state abstraction of the perturbed system dynamics is constructed and utilized for controller synthesis. In this context, our contribution is twofold: (I) We construct abstractions which model the impact of occasional high disturbance spikes on the system via so called disturbance edges. (II) We show that the application of resilient reactive synthesis techniques to these abstract models results in closed loop systems which are optimally resilient to these occasional high disturbance spikes. We have implemented this resilient ABCD workflow on top of SCOTS and showcase our method through multiple robot planning examples.

preprint2016arXiv

Dynamic Hierarchical Reactive Controller Synthesis

In the formal approach to reactive controller synthesis, a symbolic controller for a possibly hybrid system is obtained by algorithmically computing a winning strategy in a two-player game. Such game-solving algorithms scale poorly as the size of the game graph increases. However, in many applications, the game graph has a natural hierarchical structure. In this paper, we propose a modeling formalism and a synthesis algorithm that exploits this hierarchical structure for more scalable synthesis. We define local games on hierarchical graphs as a modeling formalism which decomposes a large-scale reactive synthesis problem in two dimensions. First, the construction of a hierarchical game graph introduces abstraction layers, where each layer is again a two-player game graph. Second, every such layer is decomposed into multiple local game graphs, each corresponding to a node in the higher level game graph. While local games have the potential to reduce the state space for controller synthesis, they lead to more complex synthesis problems where strategies computed for one local game can impose additional requirements on lower-level local games. Our second contribution is a procedure to construct a dynamic controller for local game graphs over hierarchies. The controller computes assume-admissible winning strategies that satisfy local specifications in the presence of environment assumptions, and dynamically updates specifications and strategies due to interactions between games at different abstraction layers at each step of the play. We show that our synthesis procedure is sound: the controller constructs a play which satisfies all local specifications. We illustrate our results through an example controlling an autonomous robot in a known, multistory building.

preprint2015arXiv

Comparing Asynchronous $l$-Complete Approximations and Quotient Based Abstractions

This paper is concerned with a detailed comparison of two different abstraction techniques for the construction of finite state symbolic models for controller synthesis of hybrid systems. Namely, we compare quotient based abstractions (QBA), with different realizations of strongest (asynchronous) $l$-complete approximations (SAlCA) Even though the idea behind their construction is very similar, we show that they are generally incomparable both in terms of behavioral inclusion and similarity relations. We therefore derive necessary and sufficient conditions for QBA to coincide with particular realizations of SAlCA. Depending on the original system, either QBA or SAlCA can be a tighter abstraction.

preprint2014arXiv

Asynchronous $l$-Complete Approximations

This paper extends the $l$-complete approximation method developed for time invariant systems to a larger system class, ensuring that the resulting approximation can be realized by a finite state machine. To derive the new abstraction method, called asynchronous $l$-complete approximation, an asynchronous version of the well-known concepts of state property, memory span and $l$-completeness is introduced, extending the behavioral systems theory in a consistent way.

preprint2014arXiv

Constructing (Bi)Similar Finite State Abstractions using Asynchronous $l$-Complete Approximations

This paper constructs a finite state abstraction of a possibly continuous-time and infinite state model in two steps. First, a finite external signal space is added, generating a so called $Φ$-dynamical system. Secondly, the strongest asynchronous $l$-complete approximation of the external dynamics is constructed. As our main results, we show that (i) the abstraction simulates the original system, and (ii) bisimilarity between the original system and its abstraction holds, if and only if the original system is $l$-complete and its state space satisfies an additional property.

preprint2014arXiv

Simulation and Bisimulation over Multiple Time Scales in a Behavioral Setting

This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and verification of large scale systems. For this new system model different notions of simulation and bisimulation are derived, ensuring that they are, respectively, preorders and equivalence relations for the system class under consideration. These relations can capture a wide selection of similarity notions available in the literature. This paper therefore provides a suitable framework for their comparison