Automated conjecturing with \emph{TxGraffiti}

TL;DR

TxGraffiti is a data-driven, heuristic-based program that automates conjecture generation in mathematics, especially in graph theory, and has contributed to numerous publications since 2017.

Contribution

The paper details the design, core principles, and new web interface of TxGraffiti, extending its application beyond graph theory.

Findings

Contributed to multiple mathematical publications since 2017.

Introduced a web-based interface for exploring conjectures.

Extended techniques to areas beyond graph theory.

Abstract

\emph{TxGraffiti} is a data-driven, heuristic-based computer program developed to automate the process of generating conjectures across various mathematical domains. Since its creation in 2017, \emph{TxGraffiti} has contributed to numerous mathematical publications, particularly in graph theory. In this paper, we present the design and core principles of \emph{TxGraffiti}, including its roots in the original \emph{Graffiti} program, which pioneered the automation of mathematical conjecturing. We describe the data collection process, the generation of plausible conjectures, and methods such as the \emph{Dalmatian} heuristic for filtering out redundant or transitive conjectures. Additionally, we highlight its contributions to the mathematical literature and introduce a new web-based interface that allows users to explore conjectures interactively. While we focus on graph theory, the techniques demonstrated extend to other areas of mathematics.