Related papers: Mining State-Based Models from Proof Corpora

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…

This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…

In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…

The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid sys- tems; however, state-of-the-art theorem provers require ex- tensive manual intervention. Furthermore, there is often a…

We introduce a resource adaptive agent mechanism which supports the user in interactive theorem proving. The mechanism uses a two layered architecture of agent societies to suggest appropriate commands together with possible command…

Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…

In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…

Simulators often provide the best description of real-world phenomena. However, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based…

Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…

This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…

Auto-active verifiers provide a level of automation intermediate between fully automatic and interactive: users supply code with annotations as input while benefiting from a high level of automation in the back-end. This paper presents…

OnlineProver is an interactive proof assistant tailored for the educational setting. Its main features include a user-friendly interface for editing and checking proofs. The user interface provides feedback directly within the derivation,…

The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…

Among formal methods, the deductive verification approach allows establishing the strongest possible formal guarantees on critical software. The downside is the cost in terms of human effort required to design adequate formal specifications…

The output of an automated theorem prover is usually presented by using a text format, they are often too heavy to be understood. In model checking setting, it would be helpful if one can observe the structure of models and the verification…

We propose to extend the Dafny system with an interactive proof mode. We present a motivating example, how the IPM works, including the main design choices we make, and a prototype implementation.

Predictions and generations from large language models are increasingly being explored as an aid in limited data regimes, such as in computational social science and human subjects research. While prior technical work has mainly explored…

Fuelled by the popularity of the transformer architecture in deep learning, several works have investigated what formal languages a transformer can learn from data. Nonetheless, existing results remain hard to compare due to methodological…

Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced…