2003/04/20 by Alexei Miasnikov, Alexei D. Miasnikov, Miasnikov, Alexei D. +3
Computer Science · Mathematics · #20F28 #68Q17 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE) #Symbolic Computation (cs.SC) #cs.NE #cs.SC #math.GR #msc:20F28 #msc:68Q17 #msc:68T05
paper · pdf · doi:10.48550/arxiv.math/0304283
29 pages, 7 figures
arxiv created 2003/04/20 · openalex publication_date 2003/04/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss a genetic version (GWA) of the Whitehead's algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead's algorithm in free groups of rank >= 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of the Whitehead's Problem in general. These experiments led us to several mathematical conjectures. If confirmed they will shed light on hidden mechanisms of Whitehead Method and geometry of automorphic orbits in free groups.