2013/09/05 by Volker Diekert, Diekert, Volker, Jonathan Kausch +1
Computer Science · Mathematics · #Algorithms and Data Compression #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #FOS: Mathematics #G.2.1 #I.1.2 #cs.DM #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1309.1290
openalex publication_date 2013/09/05 · arxiv created 2014/05/16 · arxiv updated 2014/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider three important and well-studied algorithmic problems in group theory: the word, geodesic, and conjugacy problem. We show transfer results from individual groups to graph products. We concentrate on logspace complexity because the challenge is actually in small complexity classes, only. The most difficult transfer result is for the conjugacy problem. We have a general result for graph products, but even in the special case of a graph group the result is new. Graph groups are closely linked to the theory of Mazurkiewicz traces which form an algebraic model for concurrent processes. Our proofs are combinatorial and based on well-known concepts in trace theory. We also use rewriting techniques over traces. For the group-theoretical part we apply Bass-Serre theory. But as we need explicit formulae and as we design concrete algorithms all our group-theoretical calculations are completely explicit and accessible to non-specialists.