Large Language Models (LLMs) are fast becoming indispensable tools for software developers, assisting or even partnering with them in crafting complex programs. The advantages are evident -- LLMs can significantly reduce development time, generate well-organized and comprehensible code, and occasionally suggest innovative ideas that developers might not conceive on their own. However, despite their strengths, LLMs will often introduce significant errors and present incorrect code with persuasive confidence, potentially misleading developers into accepting flawed solutions. In order to bring LLMs into the software development cycle in a more reliable manner, we propose a methodology for combining them with ``traditional'' software engineering techniques in a structured way, with the goal of streamlining the development process, reducing errors, and enabling users to verify crucial program properties with increased confidence. Specifically, we focus on the Scenario-Based Programming (SBP) paradigm -- an event-driven, scenario-based approach for software engineering -- to allow human developers to pour their expert knowledge into the LLM, as well as to inspect and verify its outputs. To evaluate our methodology, we conducted a significant case study, and used it to design and implement the Connect4 game. By combining LLMs and SBP we were able to create a highly-capable agent, which could defeat various strong existing agents. Further, in some cases, we were able to formally verify the correctness of our agent. Finally, our experience reveals interesting insights regarding the ease-of-use of our proposed approach. The full code of our case-study will be made publicly available with the final version of this paper.

PPR and Katz and is empirically smaller than Θ(1/ (αϵ )) , previously well-known for APPR. All proofs, detailed experimental settings, and related works are postponed to the appendix.

Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN verification results. However, current proofproducing verifiers do not support abstraction-based reasoning, creating a gap between scalability and provable guarantees. We address this gap by introducing a novel framework for proof-producing abstraction-based DNN verification. Our approach modularly separates the verification task into two components: (i) proving the correctness of an abstract network, and (ii) proving the soundness of the abstraction with respect to the original DNN. The former can be handled by existing proof-producing verifiers, whereas we propose the first method for generating formal proofs for the latter. This preliminary work aims to enable scalable and trustworthy verification by supporting common abstraction techniques within a formal proof framework.

The widespread adoption of deep neural networks (DNNs) requires efficient techniques for safety verification. Existing methods struggle to scale to real-world DNNs, and tremendous efforts are being put into improving their scalability. In this work, we propose an approach for improving the scalability of DNN verifiers using Conflict-Driven Clause Learning (CDCL) -- an approach that has proven highly successful in SAT and SMT solving. We present a novel algorithm for deriving conflict clauses using UNSAT proofs, and propose several optimizations for expediting it. Our approach allows a modular integration of SAT solvers and DNN verifiers, and we implement it on top of an interface designed for this purpose. The evaluation of our implementation over several benchmarks suggests a 2X--3X improvement over a similar approach, with specific cases outperforming the state of the art.

Efficient computation of graph diffusion equations (GDEs), such as Personalized PageRank, Katz centrality, and the Heat kernel, is crucial for clustering, training neural networks, and many other graph-related problems. Standard iterative methods require accessing the whole graph per iteration, making them time-consuming for large-scale graphs. While existing local solvers approximate diffusion vectors through heuristic local updates, they often operate sequentially and are typically designed for specific diffusion types, limiting their applicability. Given that diffusion vectors are highly localizable, as measured by the participation ratio, this paper introduces a novel framework for approximately solving GDEs using a local diffusion process. This framework reveals the suboptimality of existing local solvers. Furthermore, our approach effectively localizes standard iterative solvers by designing simple and provably sublinear time algorithms. These new local solvers are highly parallelizable, making them well-suited for implementation on GPUs. We demonstrate the effectiveness of our framework in quickly obtaining approximate diffusion vectors, achieving up to a hundred-fold speed improvement, and its applicability to large-scale dynamic graphs. Our framework could also facilitate more efficient local message-passing mechanisms for GNNs.

In recent years, deep reinforcement learning (DRL) approaches have generated highly successful controllers for a myriad of complex domains. However, the opaque nature of these models limits their applicability in aerospace systems and safety-critical domains, in which a single mistake can have dire consequences. In this paper, we present novel advancements in both the training and verification of DRL controllers, which can help ensure their safe behavior. We showcase a design-for-verification approach utilizing k-induction and demonstrate its use in verifying liveness properties. In addition, we also give a brief overview of neural Lyapunov Barrier certificates and summarize their capabilities on a case study. Finally, we describe several other novel reachability-based approaches which, despite failing to provide guarantees of interest, could be effective for verification of other DRL systems, and could be of further interest to the community.

In recent years, Deep Reinforcement Learning (DRL) has emerged as an effective approach to solving real-world tasks. However, despite their successes, DRL-based policies suffer from poor reliability, which limits their deployment in safety-critical domains. Various methods have been put forth to address this issue by providing formal safety guarantees. Two main approaches include shielding and verification. While shielding ensures the safe behavior of the policy by employing an external online component (i.e., a ``shield'') that overrides potentially dangerous actions, this approach has a significant computational cost as the shield must be invoked at runtime to validate every decision. On the other hand, verification is an offline process that can identify policies that are unsafe, prior to their deployment, yet, without providing alternative actions when such a policy is deemed unsafe. In this work, we present verification-guided shielding -- a novel approach that bridges the DRL reliability gap by integrating these two methods. Our approach combines both formal and probabilistic verification tools to partition the input domain into safe and unsafe regions. In addition, we employ clustering and symbolic representation procedures that compress the unsafe regions into a compact representation. This, in turn, allows to temporarily activate the shield solely in (potentially) unsafe regions, in an efficient manner. Our novel approach allows to significantly reduce runtime overhead while still preserving formal safety guarantees. We extensively evaluate our approach on two benchmarks from the robotic navigation domain, as well as provide an in-depth analysis of its scalability and completeness.

Hezbollah chief Hassan Nasrallah has issued a stern warning to Israel, threatening a war with "no restraint and no rules and no ceilings" in case of a major Israeli offensive against Lebanon. Nasrallah's remarks on Wednesday come amid soaring tensions at the Lebanon-Israel border after Israeli officials reiterated that the country is ready for an all-out war against Hezbollah. "All what the enemy says and the threats and warnings the mediators bring – and what is being said in the Israeli media – about a war in Lebanon does not scare us," Nasrallah said in a speech via video feed. He said that Israel is the party that should be "scared". Israeli Foreign Israeli Foreign Minister Israel Katz on Tuesday raised the prospect of a major conflict with the Lebanese group after Hezbollah released surveillance drone footage showing major infrastructure and military sites in northern Israel.

Rep. Randy Weber, R-Texas, joined'Fox & Friends First' to discuss the latest on what's expected with Israel's response as House lawmakers are expected to weigh several foreign aid bills this week. Israel's foreign minister on Tuesday said he is calling for additional sanctions on Iran in response to the missile and drone attack that targeted Israel over the weekend. Foreign Minister Israel Katz said he sent letters to 32 countries urging them to impose new sanctions on the Iranian missile project and declare the Islamic Revolutionary Guard Corps (IRGC) a terrorist organization. "Alongside the military response to the firing of the missiles and the UAVs, I am leading a diplomatic offensive against Iran," Katz posted on X. He said additional sanctions would "stop and weaken Iran."