Related papers: Tao's Equational Proof Challenge Accepted (Technic…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
Reasoning about the knowledge of an attacker is a necessary step in many formal analyses of security protocols. In the framework of the applied pi calculus, as in similar languages based on equational logics, knowledge is typically…
Building on the collaborative Equational Theories project initiated by Terence Tao fifteen months ago, and combining it with ideas coming from machine learning and finite model theory, we construct a latent space of equational theories…
In this paper, we develop Terence Tao's harmonic analysis method and apply it to restricted sumsets. The well known Cauchy-Davenport theorem asserts that if $A$ and $B$ are nonempty subsets of $Z/pZ$ with $p$ a prime, then $|A+B|\ge…
Most current prevalent iterative methods can be classified into the so-called extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional…
Vampire proves theorems completely automatically in first- and higher-order logic extended with theories. Proof checking is increasingly demanded to consolidate user trust in Vampires output. We describe ongoing efforts in reconstructing…
Large Language Models (LLMs) have shown remarkable reasoning capabilities through Reinforcement Learning with Verifiable Rewards (RLVR) methods. However, a key limitation of existing approaches is that rewards defined at the full trajectory…
We implement a automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation. This knowledge is then used in a Monte…
We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…
Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…
Mechanical proofs by logical relations often involve tedious reasoning about substitution. In this paper, we show that this is not necessarily the case, by developing, in Agda, a proof that all simply typed lambda calculus expressions…
Process supervision, using a trained verifier to evaluate the intermediate steps generated by a reasoner, has demonstrated significant improvements in multi-step problem solving. In this paper, to avoid the expensive effort of human…
Large language models have made significant progress in various language tasks, yet they still struggle with complex mathematics. In this paper, we propose ToRA a series of Tool-integrated Reasoning Agents designed to solve challenging…
Several successful strategies in automated reasoning rely on human-supplied guidance about which term or clause shapes are interesting. In this paper we aim to discover interesting term shapes automatically. Specifically, we discover…
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
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…
Despite recent advances in AI, the development of systems capable of executing complex, multi-step reasoning tasks involving multiple tools remains a significant challenge. Current benchmarks fall short in capturing the real-world…
In an era where we can not afford to checkpoint frequently, replication is a generic way forward to construct numerical simulations that can continue to run even if hardware parts fail. Yet, replication often is not employed on larger…