Designing robotic systems to act autonomously in unforeseen environments is a challenging task. This work presents a novel approach to use formal verification, specifically Statistical Model Checking (SMC), to verify system properties of autonomous robots at design-time. We introduce an extension of the SCXML format, designed to model system components including both Robot Operating System 2 (ROS 2) and Behavior Tree (BT) features. Further, we contribute Autonomous Systems to Formal Models (AS2FM), a tool to translate the full system model into JANI. The use of JANI, a standard format for quantitative model checking, enables verification of system properties with off-the-shelf SMC tools. We demonstrate the practical usability of AS2FM both in terms of applicability to real-world autonomous robotic control systems, and in terms of verification runtime scaling. We provide a case study, where we successfully identify problems in a ROS 2-based robotic manipulation use case that is verifiable in less than one second using consumer hardware. Additionally, we compare to the state of the art and demonstrate that our method is more comprehensive in system feature support, and that the verification runtime scales linearly with the size of the model, instead of exponentially.

It studies reasoning patterns and logical properties that are not suitably captured by classical propositional or first-order logic. Various logic formalisms have been proposed to handle deontic and normative reasoning, including systems based on modal logics (von Wright, 1951), dyadic deontic logic (Gabbay et al., 2013), and norm-based systems (Hansen, 2014). These systems differ in the properties of the obligation operator, and in their ability to consistently handle deontic paradoxes and/or norm conflicts (Gabbay et al., 2013). Input/Output (I/O) logics (Makinson & van der Torre, 2000) are a particular norm-based family of systems in which conditional norms are represented by pairs of formulas. The pairs do not carry truth-values themselves. I/O logics use an operational semantics based on detachment and come with a variety of different systems, formalized by different so-called output operators . Given a set of conditional norms N, and a set of formulas describing the situational context A, output operators produce a set of formulas that represent the obligations that are in force for that context. In order to check whether some state of affairs φ is obligatory, it suffices to check whether φ out (N, A), where out is some output operator. Unconstrained I/O logics are monotone and cannot consistently handle norm conflicts (i.e., situations in which norms with conflicting obligations are in force) without

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where algorithmic definitions enable automated generation of arbitrarily many challenging theorem-proof pairs. We demonstrate this approach on two TCS domains: Busy Beaver problems, which involve proving bounds on Turing machine halting behavior, and Mixed Boolean Arithmetic problems, which combine logical and arithmetic reasoning. Our framework automatically synthesizes problems with parallel formal (Lean4) and informal (Markdown) specifications, creating a scalable pipeline for generating verified proof challenges. Evaluation on frontier models reveals substantial gaps in automated theorem proving: while DeepSeekProver-V2-671B achieves 57.5\% success on Busy Beaver problems, it manages only 12\% on Mixed Boolean Arithmetic problems. These results highlight the difficulty of long-form proof generation even for problems that are computationally easy to verify, demonstrating the value of TCS domains for advancing automated reasoning research.

Reactive synthesis from Linear Temporal Logic over finite traces (LTLf) can be reduced to a two-player game over a Deterministic Finite Automaton (DFA) of the LTLf specification. The primary challenge here is DFA construction, which is 2EXPTIME-complete in the worst case. Existing techniques either construct the DFA compositionally before solving the game, leveraging automata minimization to mitigate state-space explosion, or build the DFA incrementally during game solving to avoid full DFA construction. However, neither is dominant. In this paper, we introduce a compositional on-the-fly synthesis framework that integrates the strengths of both approaches, focusing on large conjunctions of smaller LTLf formulas common in practice. This framework applies composition during game solving instead of automata (game arena) construction. While composing all intermediate results may be necessary in the worst case, pruning these results simplifies subsequent compositions and enables early detection of unrealizability. Specifically, the framework allows two composition variants: pruning before composition to take full advantage of minimization or pruning during composition to guide on-the-fly synthesis. Compared to state-of-the-art synthesis solvers, our framework is able to solve a notable number of instances that other solvers cannot handle. A detailed analysis shows that both composition variants have unique merits.

Statement autoformalization, the automated translation of statements from natural language into formal languages, has become a subject of extensive research, yet the development of robust automated evaluation metrics remains limited. Existing evaluation methods often lack semantic understanding, face challenges with high computational costs, and are constrained by the current progress of automated theorem proving. To address these issues, we propose GTED (Generalized Tree Edit Distance), a novel evaluation framework that first standardizes formal statements and converts them into operator trees, then determines the semantic similarity using the eponymous GTED metric. Across the miniF2F and ProofNet benchmarks, GTED consistently ranks as a top-performing metric, achieving the highest accuracy and Kappa on miniF2F and the joint-highest accuracy on ProofNet. This strong overall performance provides the community with a computationally lightweight and more faithful metric for automated evaluation. The code and experimental results are available at https://github.com/XiaoyangLiu-sjtu/GTED.

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's founda-tional logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. In recent years, Large Language Models (LLMs) have made significant progress in mathematical reasoning, particularly in automated theorem proving (Bibel, 2013). Formal theorem proving is a crucial domain for ensuring the correctness of hard-to-verify proofs within theorem proving. Lean 4 (Moura & Ullrich, 2021), as a prominent proof assistant, provides a solid foundation for algebra and number theory through its extensive Mathlib library (mathlib community, 2020). It has been widely used in the formal verification of theorems within LLMs. However, Euclidean geometry, an essential component of mathematical reasoning and a frequent focus of competitions, remains relatively underexplored in Lean 4 community, Mathlib and automated theorem provers.

We propose a neurosymbolic approach to the explanation of complex sequences of decisions that combines the strengths of decision procedures and Large Language Models (LLMs). We demonstrate this approach by producing explanations for the solutions of Hitori puzzles. The rules of Hitori include local constraints that are effectively explained by short resolution proofs. However, they also include a connectivity constraint that is more suitable for visual explanations. Hence, Hitori provides an excellent testing ground for a flexible combination of SAT solvers and LLMs. We have implemented a tool that assists humans in solving Hitori puzzles, and we present experimental evidence of its effectiveness.

We present a category theoretical formulation of the Monetary Macroeconomic Accounting Theory (MoMaT) of Menéndez and Winschel [2025]. We take macroeconomic (national) accounting systems to be composed from microeconomic double-entry systems with real and monetary units of accounts. Category theory is the compositional grammar and module system of mathematics which we use to lift micro accounting consistency to the macro level. The main function of money in MoMaT is for the repayment of loans and not for the exchange of goods, bridging the desynchronisation of input and output payments of producers. Accordingly, temporal accounting consistency is at the macroeconomic level. We show that the accounting for macroeconomies organised by a division of labor can be consistent and stable as a prerequisite for risk and GDP sharing of societies. We exemplify the theory by five sectoral agents of Labor and Resource owners, a Company as the productive sector, a Capitalist for profits, and a Bank as the financial sector providing loans to synchronise the micro and the macro levels of an economy. The dynamics is described by eight sectoral macroeconomic bookings in each period demonstrating stable convergence of the MoMaT in numerical simulations. The categorical program implements a consistent evolution of hierarchical loan repayment contracts by an endofunctor. The universal constructions of a limit verify all constraints as the sectoral investment and learning function at the macroeconomic level. The dual colimit computes the aggregated informations at the macro level as usual in the mathematics of transitions from local to global structures. We use visual diagrams to make complex economic relationships intuitive. This paper is meant to map economic to categorical concepts to enable interdisciplinary collaboration for digital twins of monetary accounting systems.

The automation of logic circuit design enhances chip performance, energy efficiency, and reliability, and is widely applied in the field of Electronic Design Automation (EDA).And-Inverter Graphs (AIGs) efficiently represent, optimize, and verify the functional characteristics of digital circuits, enhancing the efficiency of EDA development.Due to the complex structure and large scale of nodes in real-world AIGs, accurate modeling is challenging, leading to existing work lacking the ability to jointly model functional and structural characteristics, as well as insufficient dynamic information propagation capability.To address the aforementioned challenges, we propose AIGer.Specifically, AIGer consists of two components: 1) Node logic feature initialization embedding component and 2) AIGs feature learning network component.The node logic feature initialization embedding component projects logic nodes, such as AND and NOT, into independent semantic spaces, to enable effective node embedding for subsequent processing.Building upon this, the AIGs feature learning network component employs a heterogeneous graph convolutional network, designing dynamic relationship weight matrices and differentiated information aggregation approaches to better represent the original structure and information of AIGs.The combination of these two components enhances AIGer's ability to jointly model functional and structural characteristics and improves its message passing capability. Experimental results indicate that AIGer outperforms the current best models in the Signal Probability Prediction (SSP) task, improving MAE and MSE by 18.95\% and 44.44\%, respectively. In the Truth Table Distance Prediction (TTDP) task, AIGer achieves improvements of 33.57\% and 14.79\% in MAE and MSE, respectively, compared to the best-performing models.

However, the availability of such real-world SA T formulas is limited.