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Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
Contemporary AI systems achieve extraordinary performance yet remain opaque and non-verifiable, creating a crisis of trust for safety-critical deployment. We introduce MathLedger, a substrate for verifiable machine cognition that integrates…
Formal methods yet advantageous, face challenges towards wide acceptance and adoption in software development practices. The major reason being presumed complexity. The issue can be addressed by academia with a thoughtful plan of teaching…
Neural network controllers have shown potential in achieving superior performance in feedback control systems. Although a neural network can be trained efficiently using deep and reinforcement learning methods, providing formal guarantees…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Developing and fielding complex systems requires proof that they are reliably correct with respect to their design and operating requirements. Especially for autonomous systems which exhibit unanticipated emergent behavior, fully…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Machine learning has emerged as a significant approach to efficiently tackle electronic structure problems. Despite its potential, there is less guarantee for the model to generalize to unseen data that hinders its application in real-world…
In mathematical proof education, there remains a need for interventions that help students learn to write mathematical proofs. Research has shown that timely feedback can be very helpful to students learning new skills. While for many years…
Despite the tremendous advances that have been made in the last decade on developing useful machine-learning applications, their wider adoption has been hindered by the lack of strong assurance guarantees that can be made about their…
Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
Reasoning about safety, security, and other dependability attributes of autonomous systems is a challenge that needs to be addressed before the adoption of such systems in day-to-day life. Formal methods is a class of methods that…
Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications,…
GraphFlow is a visual workflow system designed to improve the reliability of agentic AI automation in multi-step, mission-critical processes. In these workflows, small errors compound rapidly: under an idealized model of independent steps,…
Autonomous systems -- such as self-driving cars, autonomous drones, and automated trains -- must come with strong safety guarantees. Over the past decade, techniques based on formal methods have enjoyed some success in providing strong…