Abstract: A classical difficult isomorphism testing problem is to test isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. It is known that this problem can be ...

The legendary graph isomorphism problem may be harder than a 2015 result seemed to suggest. “In Laci Babai, you have one of the most legendary and fearsome theoretical computer scientists there ever ...

A puzzle that has long flummoxed computers and the scientists who program them has suddenly become far more manageable. A new algorithm efficiently solves the graph isomorphism problem, computer ...

For decades, the graph isomorphism problem has held a special status within complexity theory. While thousands of other computational problems have meekly succumbed to categorization as either hard or ...

Abstract: We study the complexity of the isomorphism and automorphism problems for finite rings with unity. We show that both integer factorization and graph isomorphism reduce to the problem of ...

An innovative approach to solving a stubborn, but elementary, question in graph theory — the mathematical study of networks of nodes and their connections — may signal the first major theoretical ...

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm. The back and forth ...

I applied GRPO to teach Qwen2.5-1.5B-Instruct to solve graph isomorphism. The base model has 0% accuracy on the task (it always outputs "NOT ISOMORPHIC" in 2 tokens), which means GRPO gets zero reward ...

Algebraic structures form the backbone of modern abstract algebra, encapsulating a wide range of systems such as groups, rings, fields, and modules, each characterised by distinct axiomatic properties ...