Details

Autor(en) / Beteiligte

• Fiala, Jirí
• Koubek, Václav
• Kratochvíl, Jan

Titel

The Complexity of Equivalence and Isomorphism of Systems of Equations over Finite Groups

Ist Teil von

• Lecture notes in computer science, 2004, Vol.3153, p.380-391

Ort / Verlag

Germany: Springer Berlin / Heidelberg

Erscheinungsjahr

2004

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study the computational complexity of the isomorphism and equivalence problems on systems of equations over a fixed finite group. We show that the equivalence problem is in P if the group is Abelian, and coNP-complete if the group is non-Abelian. We prove that if the group is non-Abelian, then the problem of deciding whether two systems of equations over the group are isomorphic is coNP-hard. If the group is Abelian, then the isomorphism problem is graph isomorphism hard. Moreover, if we impose the restriction that all equations are of bounded length, then we prove that the isomorphism problem for systems of equations over finite Abelian groups is graph isomorphism complete. Finally we prove that the problem of counting the number of isomorphisms of systems of equations is no harder than deciding whether there exist any isomorphisms at all.