Related papers: Mining State-Based Models from Proof Corpora

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…

Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…

We present an interactive version of an evidence-driven state-merging (EDSM) algorithm for learning variants of finite state automata. Learning these automata often amounts to recovering or reverse engineering the model generating the data…

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…

Models such as finite state automata are widely used to abstract the behavior of software systems by capturing the sequences of events observable during their execution. Nevertheless, models rarely exist in practice and, when they do, get…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

Latent state space models are a fundamental and widely used tool for modeling dynamical systems. However, they are difficult to learn from data and learned models often lack performance guarantees on inference tasks such as filtering and…

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…

Congruence closure procedures are used extensively in automated reasoning and are a core component of most satisfiability modulo theories solvers. However, no known congruence closure algorithms can support any of the expressive logics…

We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…

Trustworthy machine learning is of primary importance to the practical deployment of deep learning models. While state-of-the-art models achieve astonishingly good performance in terms of accuracy, recent literature reveals that their…

Large language models have the potential to simplify formal theorem proving and make it more accessible. But how to get the most out of these models is still an open question. To answer this question, we take a step back and explore the…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

We address the problem of translating informal mathematical proofs expressed in natural language into formal proofs in Lean4 under a constrained computational budget. Our approach is grounded in two key insights. First, informal proofs tend…

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…

When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…

Data attribution methods aim to answer useful counterfactual questions like "what would a ML model's prediction be if it were trained on a different dataset?" However, estimation of data attribution models through techniques like empirical…

Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…

We prove the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. This is accomplished by emulating an effective algorithm via an abstract state machine, and simulating such an abstract…

Many practical problems can be understood as the search for a state of affairs that extends a fixed partial state of affairs, the \emph{environment}, while satisfying certain conditions that are formally specified. Such problems are found…