Related papers: Metamath Zero: The Cartesian Theorem Prover
LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…
Verifiable delay functions have found a lot of applications in blockchain technology in recent times. Continuous verifiable delay functions are an improvement over the basic notion of VDFs with recursive capabilities. We are proposing the…
In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing…
Protecting secrets is a key challenge in our contemporary information-based era. In common situations, however, revealing secrets appears unavoidable, for instance, when identifying oneself in a bank to retrieve money. In turn, this may…
This paper presents the verification of control systems implemented in Simulink. The goal is to ensure that high-level requirements on control performance, like stability, are satisfied by the Simulink diagram. A two stage process is…
There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
This paper presents a {theoretical study} of the problem of verifying linearizability at runtime, where one seeks for a concurrent algorithm for verifying that the current execution of a given concurrent shared object implementation is…
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…
This paper presents our system for Task 3 of the CLEF 2025 CheckThat! Lab, which focuses on verifying numerical and temporal claims using retrieved evidence. We explore two complementary approaches: zero-shot prompting with…
Control barrier functions are a popular method of ensuring system safety, and these functions can be used to enforce invariance of a set under the dynamics of a system. A control barrier function must have certain properties, and one must…
I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…
As AI models become ubiquitous in our daily lives, there has been an increasing demand for transparency in ML services. However, the model owner does not want to reveal the weights, as they are considered trade secrets. To solve this…
Recent advances in large language models show strong promise for formal reasoning. However, most LLM-based theorem provers have long been constrained by the need for expert-written formal statements as inputs, limiting their applicability…
In the past decade, many techniques have been developed to prove linearizability, the gold standard of correctness for concurrent data structures. Intuitively, linearizability requires that every operation on a concurrent data structure…
This article introduces a fully automated verification technique that permits to analyze real-time systems described using a continuous notion of time and a mixture of operational (i.e., automata-based) and descriptive (i.e., logic-based)…
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…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…