Abstract The TLA $$^+$$ + language has been widely used, both in academia and industry, to specify and reason about distributed systems. This paper presents Apalache , an efficient and flexible symbolic model checker for TLA $$^+$$ + . Apalache ’s engine is based on bounded model checking, with symbolic transitions being extracted from TLA $$^+$$ + specifications and verification conditions suitable for satisfiability modulo theories (SMT) solvers being generated from them. Reasoning can be done in terms of safety and liveness properties, with liveness checking realised via a liveness-to-safety reduction. Apalache ’s flexibility lies in its three complementary functionalities: bounded exhaustive verification, for bounded guarantees, randomised symbolic execution, for prototyping and bug detection, and inductiveness checking, for unbounded guarantees. The paper describes Apalache ’s architecture and features, including its support for PlusCal and Quint, two languages that share the same semantic foundation as TLA $$^+$$ + . Industrial usage of Apalache is also presented, together with a case study which illustrates how Apalache can be used to verify the agreement property of a consensus protocol.

Over the past years, distributed consensus research has expanded its focus to address challenges in large-scale, permissionless systems, such as blockchains. This shift reflects the need to accommodate dynamic participation, in contrast to the traditional model of a static set of continuously online validators. Works like Bitcoin and the sleepy model have laid the groundwork for this evolving framework.Notable contributions by Momose and Ren (CCS 2022), along with subsequent research, have introduced Total-Order Broadcast protocols that leverage Graded Agreement primitives and support dynamic participation. However, these approaches often require multiple phases of voting per decision, which can create a bottleneck for real-world, large-scale systems.To address this, our paper introduces TOB-SVD, a novel TotalOrder Broadcast protocol in the sleepy model that is resilient to up to 1/2 Byzantine validators. TOB-SVD requires only a single phase of voting per decision in the best case and achieves lower expected latency compared to existing approaches offering the same optimal adversarial resilience. This work paves the way for more practical Total-Order Broadcast protocols that can be implemented in real-world systems involving a large number of validators with fluctuating participation over time.

The pervasive spread of multimedia misinformation and disinformation presents a significant challenge to information integrity, demanding robust and efficient verification methodologies. Accurately assessing the authenticity and context of complex multimedia content across diverse platforms requires advanced analytical capabilities. This work introduces Ægis, a novel AI-enhanced solution developed as the authors' submission to the ACMMM'25 - Grand Challenge on Multimedia Verification, aimed at improving the efficiency of multimedia verification. The proposed solution integrates both state-of-the-art and traditional verification tools to comprehensively address various aspects of verification tasks, including event summarization, forensic analysis, and evidence validation. In addition to selectively applied verification modules, large language models (LLMs) are leveraged extensively to fuse findings, perform reasoning, and generate structured verification reports-significantly streamlining the verification process. Demonstrated on the competition multimedia dataset, Ægis accurately validates content integrity, extracts geospatial and temporal information, and identifies content origin across platforms, offering reliable and ethical support for real-world fact-checking.