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We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…
A commonly observed problem with the state-of-the art abstractive summarization models is that the generated summaries can be factually inconsistent with the input documents. The fact that automatic summarization may produce…
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…
This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time…
We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…
Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…
Agentic AI systems execute a sequence of actions, such as reasoning steps or tool calls, in response to a user prompt. To evaluate the success of their trajectories, researchers have developed verifiers, such as LLM judges and…
Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for…
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…
We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum…
The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express…
Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers…
Boson-Sampling holds the potential to experimentally falsify the Extended Church Turing thesis. The computational hardness of Boson-Sampling, however, complicates the certification that an experimental device yields correct results in the…
In recent years, program verifiers and interactive theorem provers have become more powerful and more suitable for verifying large programs or proofs. This has demonstrated the need for improving the user experience of these tools to…
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…
Super learner algorithm can be applied to combine results of multiple base learners to improve quality of predictions. The default method for verification of super learner results is by nested cross validation. It has been proposed by…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
In order to increase user confidence, many automated theorem provers provide certificates that can be independently verified. In this paper, we report on our progress in developing a standalone tool for checking the correctness of…