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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…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves…
We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…
Formal verification is a promising method for producing reliable software, but the difficulty of manually writing verification proofs severely limits its utility in practice. Recent methods have automated some proof synthesis by guiding a…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
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…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
Formal verification using proof assistants, such as Coq, is an effective way of improving software quality, but requires significant effort and expertise. Machine learning can automatically synthesize proofs, but such tools are able to…
Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary…
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…
Formal verification is increasingly recognized as a critical foundation for building reliable software systems. However, the need for specialized expertise to write precise specifications, navigate complex proof obligations, and learn…
Formal verification tools are often developed by experts for experts; as a result, their usability by programmers with little formal methods experience may be severely limited. In this paper, we discuss this general phenomenon with…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…
Design verification is a complex and costly task, especially for large and intricate processor projects. Formal verification techniques provide advantages by thoroughly examining design behaviors, but they require extensive labor and…
Many verification tools come out of academic projects, whose natural constraints do not typically lead to a strong focus on usability. For widespread use, however, usability is essential. Using a well-known benchmark, the Tokeneer problem,…
Foundational verification allows programmers to build software which has been empirically shown to have high levels of assurance in a variety of important domains. However, the cost of producing foundationally verified software remains…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…