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- W1984697719 abstract "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 G RAPH I SOMORPHISM -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 G RAPH I SOMORPHISM -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." @default.
- W1984697719 created "2016-06-24" @default.
- W1984697719 creator A5007869716 @default.
- W1984697719 date "2005-11-01" @default.
- W1984697719 modified "2023-09-27" @default.
- W1984697719 title "The complexity of equivalence and isomorphism of systems of equations over finite groups" @default.
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- W1984697719 doi "https://doi.org/10.1016/j.tcs.2005.07.018" @default.
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