Tootfinder

The Complexity of Defining and Separating Fixpoint Formulae in Modal Logic
Jean Christoph Jung, J\k{e}drzej Ko{\l}odziejski
https://arxiv.org/abs/2509.24583 https://

The Complexity of Defining and Separating Fixpoint Formulae in Modal Logic
Modal separability for modal fixpoint formulae is the problem to decide for two given modal fixpoint formulae $φ,φ'$ whether there is a modal formula $ψ$ that separates them, in the sense that $φ\modelsψ$ and $ψ\models\negφ'$. We study modal separability and its special case modal definability over various classes of models, such as arbitrary models, finite models, trees, and models of bounded outdegree. Our main results are that modal separability is PSpace-complete over words, that is,…

PAT-Agent: Autoformalization for Model Checking
Xinyue Zuo, Yifan Zhang, Hongshu Wang, Yufan Cai, Zhe Hou, Jing Sun, Jin Song Dong
https://arxiv.org/abs/2509.23675 https://

PAT-Agent: Autoformalization for Model Checking
Recent advances in large language models (LLMs) offer promising potential for automating formal methods. However, applying them to formal verification remains challenging due to the complexity of specification languages, the risk of hallucinated output, and the semantic gap between natural language and formal logic. We introduce PAT-Agent, an end-to-end framework for natural language autoformalization and formal model repair that combines the generative capabilities of LLMs with the rigor of fo…

Rademacher-type exact formula and higher order Tur\'{a}n inequalities for cubic overpartitions
Archit Agarwal, Meghali Garg, Bibekananda Maji
https://arxiv.org/abs/2509.23151

Rademacher-type exact formula and higher order Turán inequalities for cubic overpartitions
In 1918, Hardy and Ramanujan made a breakthrough by developing the circle method to deduce an asymptotic formula for the partition function $p(n)$, which was later refined by Rademacher in 1937 to produce an absolutely convergent series representation for $p(n)$. Since then, Rademacher-type exact formulas for various partition functions have been investigated by many mathematicians. The concept of overpartitions was introduced by Lovejoy and Corteel in 2004. Kim, in 2010, studied an overpartiti…

Correlated double ramification cycle formula
Thomas Blomme, Francesca Carocci
https://arxiv.org/abs/2509.24721 https://arxiv.org/pdf/2509.24721

Correlated double ramification cycle formula
We prove a refinement of Pixton's formula for the double ramification cycle with target variety which takes into account the correlator of a rubber map previously introduced by the authors. To do so, we need to: reinterpret the correlator in terms of (logarithmic) roots of the trivial line bundle; refine the natural stratification of the boundary of moduli of maps to keep track of how torsion line bundles on the target variety pull-back. We apply the refined DR cycle formula to compute 0-correl…

Ontology is shaping up to be the buzzword of 2026 because they are offering what #LLMs are lacking: formal grounding
LLMs offer creativity but need logical grounding. Ontologies provide this formal structure, anchoring meaning and unifying diverse data sources into a single semantic layer. They are essential for achieving precision and are one of the most reliable defense mechanisms against

Tree-based formulation for the multi-commodity flow problem
Simon Spoorendonk, Bj{\o}rn Petersen
https://arxiv.org/abs/2509.24656 https://arxiv.org/pdf/250…

Tree-based formulation for the multi-commodity flow problem
We introduce a tree-based formulation for the minimum-cost multi-commodity flow problem that addresses large-scale instances. The method decomposes the source-based model by representing flows as convex combinations of trees rooted at source nodes, and solves the resulting formulation with column generation. The number of demand constraints now depends on the number of sources $|S|$, not commodities $|K|$, yielding a compact master problem when $|S| \ll |K…

(€) In #Rothenfels wird es kein #Bürgerbegehren gegen den geplanten #Windpark geben.
Die eingereichten Unterschriften reichten nicht aus, zudem passte die Formulierung des Begehren…

Rothenfels: Nicht genügend Unterschriften: Kein Bürgerbegehren gegen den Windpark in Rothenfels
Bei einer Sondersitzung kurz vor Weihnachten machte der Leiter der Verwaltungsgemeinschaft deutlich, dass die Formulierung des Bürgerbegehrens nicht zu den Gegebenheiten in Rothenfels passt.

Bridging Language Models and Formal Methods for Intent-Driven Optical Network Design
Anis Bekri, Amar Abane, Abdella Battou, Saddek Bensalem
https://arxiv.org/abs/2509.22834 htt…

Bridging Language Models and Formal Methods for Intent-Driven Optical Network Design
Intent-Based Networking (IBN) aims to simplify network management by enabling users to specify high-level goals that drive automated network design and configuration. However, translating informal natural-language intents into formally correct optical network topologies remains challenging due to inherent ambiguity and lack of rigor in Large Language Models (LLMs). To address this, we propose a novel hybrid pipeline that integrates LLM-based intent parsing, formal methods, and Optical Retrieval…

Local Success Does Not Compose: Benchmarking Large Language Models for Compositional Formal Verification
Xu Xu, Xin Li, Xingwei Qu, Jie Fu, Binhang Yuan
https://arxiv.org/abs/2509.23061

Local Success Does Not Compose: Benchmarking Large Language Models for Compositional Formal Verification
We introduce DafnyCOMP, a benchmark for evaluating large language models (LLMs) on compositional specification generation in Dafny. Unlike prior benchmarks that focus on single-function tasks, DafnyCOMP targets programs composed of multiple interacting functions with data dependencies, requiring reasoning across component boundaries. The benchmark consists of 300 automatically synthesized multi-function programs. We evaluate several state-of-the-art LLM families and find that, while they perfor…

Quasi-Ergodic Control of Multi-Periodic Autoregressive Processes: Formulation and Examples
Vyacheslav Kungurtsev
https://arxiv.org/abs/2509.24729 https://a…

Quasi-Ergodic Control of Multi-Periodic Autoregressive Processes: Formulation and Examples
This work considers state dynamics driven by Periodic Autoregressive Moving Average noise, and control of the system over time. Such processes appear frequently in applications involving the environment, such as energy and agriculture. Managing these systems applying forecasts to make decisions that exhibit foresight and risk aversion while maximizing profits is a challenging control problem that can be computationally difficult for standard scenario- based methods. This paper presents a formul…