https://logic.kastel.kit.edu/offers/Recent content in Offers on Logic of Autonomous Dynamical SystemsHugoen-ushttps://logic.kastel.kit.edu/offers/2024-brieger-ma-verification/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2024-brieger-ma-verification/https://logic.kastel.kit.edu/offers/2024-abouelwafa-automatic-model-quality-evaluation/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2024-abouelwafa-automatic-model-quality-evaluation/https://logic.kastel.kit.edu/offers/2025-butte-ba-dglsc-case-study/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-butte-ba-dglsc-case-study/Cyber-phyiscal systems (CPS) like trains, planes, autonomous cars or robots need verification to ensure their safety. Especially relevant are situations involving two CPSs, as these situations occur frequently in real-world. The challenging aspects here are the possible interactions between the CPSs that arise from their intentions or goals. The logic dGLsc which has been developed in our group, deals with these situations by regarding them as games and the involved CPSs as players, each with an individual goal they try to reach.https://logic.kastel.kit.edu/offers/2025-butte-ma-dglsc-case-study/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-butte-ma-dglsc-case-study/Cyber-phyiscal systems (CPS) like trains, planes, autonomous cars or robots need verification to ensure their safety. Especially relevant are situations involving two CPSs, as these situations occur frequently in real-world. The challenging aspects here are the possible interactions between the CPSs that arise from their intentions or goals. The logic dGLsc which has been developed in our group, deals with these situations by regarding them as games and the involved CPSs as players, each with an individual goal they try to reach.https://logic.kastel.kit.edu/offers/2026-brieger-keymaerax/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2026-brieger-keymaerax/KeYmaera X is an interactive theorem prover for hybrid systems. We are looking for students who are curious about bridging the theory and practice of theorem proving and helping maintain the KeYmaera X prover codebase. We are open to students’ own ideas for improvements and also have many ideas we would be happy to discuss together. For more information, please reach out to brieger@kit.edu.https://logic.kastel.kit.edu/offers/2025-hellwig-pendulum/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-hellwig-pendulum/Chaotic systems like the double pendulum are highly sensitive to initial conditions, making their long-term behavior unpredictable. This project explores how differential dynamic logic (dL) and differential invariants can be used to formally analyze such systems. You will investigate which properties of the double pendulum can be proven within dL, leveraging mathematical logic to uncover structure in chaos. If you’re interested in dynamical systems and formal methods this project offers a unique challenge at the intersection of logic and physics.https://logic.kastel.kit.edu/offers/2025-butte-dglsc-modifications/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-butte-dglsc-modifications/Cyber-phyiscal systems (CPS) like trains, planes, autonomous cars or robots need verification to ensure their safety. Especially relevant are situations involving two CPSs, as these situations occur frequently in real-world. The challenging aspects here are the possible interactions between the CPSs that arise from their intentions or goals. The logic dGLsc which has been developed in our group, deals with these situations by regarding them as games and the involved CPSs as players, each with an individual goal they try to reach.https://logic.kastel.kit.edu/offers/2026-brieger-ma-formalization-of-marine-traffic-rules/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2026-brieger-ma-formalization-of-marine-traffic-rules/On the sea, marine traffic rules regulate how vessels must behave when they are close to other ships to avoid collisions. Autonomous vessels implement collision avoidance based on mathematically formalized versions of these rules. However, this only guarantees safety if the rules themselves are sufficient to prevent collisions. The goal of this master thesis is to formalize both the dynamics of ships and the marine traffic rules, and to prove that if ships follow the rules, no collisions can occur.https://logic.kastel.kit.edu/offers/2025-laurent-llm-lean/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-laurent-llm-lean/Proof assistants like Lean require substantial human effort to guide proof construction. However, recent advances in machine learning, particularly with Large Language Models (LLMs), suggest new possibilities for automation. This project will explore how LLMs can iteratively refine natural language proofs into formal proofs, reducing the manual effort required for formalization. Using the Delphyne framework – which introduces a new foundational paradigm for building modular and reliable LLM-enabled software – you will develop a pipeline for formalizing mathematical arguments in Lean, using a creative combination of prompting, search and domain-specific knowledge.https://logic.kastel.kit.edu/offers/2025-butte-keymaera-implementation/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-butte-keymaera-implementation/Cyber-phyiscal systems (CPS) like trains, planes, autonomous cars or robots need verification to ensure their safety. Especially relevant are situations involving two CPSs, as these situations occur frequently in real-world. The challenging aspects here are the possible interactions between the CPSs that arise from their intentions or goals. The logic dGLsc which has been developed in our group, deals with these situations by regarding them as games and the involved CPSs as players, each with an individual goal they try to reach.https://logic.kastel.kit.edu/offers/20205-hellwig-sstl/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/20205-hellwig-sstl/Project Description This project focuses on building a Domain Specific Language (DSL) in Julia based on Signal Spatio-Temporal Logic (SSTL). SSTL allows us to verify if complex physical systems such as power grids or traffic networks meet safety requirements over time and space. The student will design a flexible syntax allowing users to define these requirements independent of network topology. Crucially, the student will implement this logic with differentiable semantics. Unlike standard logic (which returns a simple True/False), this approach calculates a continuous robustness score.https://logic.kastel.kit.edu/offers/2024-abouelwafa-implementing-da/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2024-abouelwafa-implementing-da/The goal of this project is to understand, design and implement invariant checking algorithms based on differential algebraic methods with a computer algebra system. The starting point is this paper and will involve a translation of the theoretical results into a practical implementation in a computer algebra system. See the BLAD differential algebra package.https://logic.kastel.kit.edu/offers/2023-phd-positions/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2023-phd-positions/https://logic.kastel.kit.edu/offers/2024-laurent-llm-program-synthesis/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2024-laurent-llm-program-synthesis/Large Language Models like GPT-4 have driven breakthroughs in program synthesis and power widely used coding assistants such as GitHub Copilot. Yet, their lack of reliability has limited their practical impact and prevented them from solving large-scale software development challenges that require chaining many steps of editing or reasoning without error. This project will investigate the combination of Large Language Models (LLMs) with proof assistants such as Why3, KeY, and Dafny, which are capable of rigorously reasoning about programs and establishing their correctness.https://logic.kastel.kit.edu/offers/2025-hellwig-chaos/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-hellwig-chaos/Chaotic systems are notoriously difficult to analyze, yet they appear in many real-world applications. This project explores how differential dynamic logic (dL) can be used to formally understand chaos: Can we detect chaotic behavior? How can we characterize attractors of these systems? And how do these properties impact safety guarantees? If you’re interested in formal methods, dynamical systems, and chaos theory, this project offers a deep dive into the logical structure of unpredictability.https://logic.kastel.kit.edu/offers/2025-hellwig-visualization/Mon, 01 Jan 0001 00:00:00 +0000https://logic.kastel.kit.edu/offers/2025-hellwig-visualization/When proving system properties in differential dynamic logic (dL), it’s often unclear whether a failed proof attempt is due to an actual system flaw or a missing proof step. Counterexamples can help, but understanding them in the abstract is challenging. This project explores integrating visualization tools to make counterexamples more intuitive, bridging the gap between formal reasoning and system behavior. If you’re interested in formal methods, visualization, and dynamical systems, this is a great opportunity to make proofs more insightful and interactive.