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In our daily lives and industrial settings, we often encounter dynamic problems that require reasoning over time and metric constraints. These include tasks such as scheduling, routing, and production sequencing. Dynamic logics have…
The search for increased trustworthiness of SAT solvers is very active and uses various methods. Some of these methods obtain a proof from the provers then check it, normally by replicating the search based on the proof's information.…
Tool-augmented Large Language Models (TALMs) are known to enhance the skillset of large language models (LLMs), thereby, leading to their improved reasoning abilities across many tasks. While, TALMs have been successfully employed in…
Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
Solving mathematical word problems (MWPs) automatically is challenging, primarily due to the semantic gap between human-readable words and machine-understandable logics. Despite the long history dated back to the1960s, MWPs have regained…
We provide a complete enumeration of all complex Golay pairs of length up to 25, verifying that complex Golay pairs do not exist in lengths 23 and 25 but do exist in length 24. This independently verifies work done by F. Fiedler in 2013…
Model counting ($\#\text{SAT}$) is a fundamental yet $\#\text{P}$-complete problem central to probabilistic reasoning. In this work, we address \textit{incremental model counting}, where sequences of structurally similar formulas must be…
We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture…
We present a comprehensive demonstration of how automated reasoning can assist mathematical research, both in the discovery of conjectures and in their verification. Our focus is a discrete geometry problem: What is $\mu_{5}(n)$, the…
Large Language Models (LLMs) hold significant promise for mathematics education, yet they often struggle with complex mathematical reasoning. While Retrieval-Augmented Generation (RAG) mitigates these issues by grounding LLMs in external…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
State-of-the-art SAT solvers are nowadays able to handle huge real-world instances. The key to this success is the so-called Conflict-Driven Clause-Learning (CDCL) scheme, which encompasses a number of techniques that exploit the conflicts…
Quantitative analysis of computing systems is an emerging area in automated formal analysis. Such properties address aspects such as costs and rewards, quality measures, resource consumption, distance metrics, etc. Existing solutions for…
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics…
Symbiotic Autonomous Systems (SAS) are advanced intelligent and cognitive systems exhibiting autonomous collective intelligence enabled by coherent symbiosis of human-machine interactions in hybrid societies. Basic research in the emerging…
Machine learning is a thriving part of computer science. There are many efficient approaches to machine learning that do not provide strong theoretical guarantees, and a beautiful general learning theory. Unfortunately, machine learning…
Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system…
Assurance cases offer a structured way to present arguments and evidence for certification of systems where safety and security are critical. However, creating and evaluating these assurance cases can be complex and challenging, even for…
Large Language Models (LLMs) excel in language tasks but are prone to hallucinations and outdated knowledge. Retrieval-Augmented Generation (RAG) mitigates these by grounding LLMs in external knowledge. However, in complex domains involving…