The Word Problem in the Baumslag group with a non-elementary Dehn function is polynomial time decidable

TL;DR

This paper proves that the Word problem in the Baumslag group G(1,2), known for its complex Dehn function, can be decided efficiently within polynomial time, challenging previous assumptions about its computational difficulty.

Contribution

It establishes the polynomial-time decidability of the Word problem in a specific Baumslag group with a non-elementary Dehn function, a novel result in group theory.

Findings

Word problem in G(1,2) is polynomial-time decidable

Challenges the belief that non-elementary Dehn functions imply high computational complexity

Provides new insights into algorithmic properties of complex groups

Abstract

We prove that the Word problem in the Baumslag group G(1,2) which has a non-elementary Dehn function is decidable in polynomial time.