Compressed words and automorphisms in fully residually free groups

TL;DR

This paper proves that the compressed word problem and the automorphism group word problem in finitely-generated fully residually free groups are decidable in polynomial time, advancing computational group theory.

Contribution

It establishes polynomial-time decidability for the compressed word problem and automorphism group word problem in F-groups, a significant step in understanding their algorithmic properties.

Findings

Compressed word problem is decidable in polynomial time.

Word problem in automorphism groups is decidable in polynomial time.

Results improve computational understanding of fully residually free groups.

Abstract

We show that the compressed word problem in a finitely-generated fully residually free group (F -group) is decidable in polynomial time, and use the result to show that the word problem in the automorphism group of such a group is decidable in polynomial time.