2007/12/04 by Marc Autord, Autord, Marc
Computer Science · Mathematics · #20M05 #68Q42 #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Polynomial and algebraic computation #math.GR #msc:20M05 #msc:68Q42 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0712.0525
arxiv created 2007/12/04 · openalex publication_date 2007/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gröbner bases, in their noncommutative version, and word reversing are methods for solving the word problem of a presented monoid, and both rely on iteratively completing the initial list of relations. Simple examples may suggest to conjecture that both completion procedures are closely related. Here we disprove this conjecture by exhibiting families of presentations for which they radically differ.