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The complexity of equivalence and isomorphism of systems of equations over finite groups
Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
2004 (English)In: Mathematical Foundations of Computer Science 2004: 29th International Symposium, MFCS 2004, Prague, Czech Republic, August 22-27, 2004. Proceedings / [ed] Jirí Fiala, Václav Koubek and Jan Kratochvíl, Springer Berlin/Heidelberg, 2004, Vol. 3153, 380-391 p.Chapter in book (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2004. Vol. 3153, 380-391 p.
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online) ; 3153
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-48283DOI: 10.1007/978-3-540-28629-5_28ISBN: 3-540-22823-3ISBN: 978-3-540-22823-3ISBN: 978-3-540-28629-5OAI: diva2:269179
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-11-06Bibliographically approved

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