On truth-table reducibility to SAT
Information and Computation
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
The Formula Isomorphism Problem
SIAM Journal on Computing
The complexity of solving equations over finite groups
Information and Computation
Equivalence and Isomorphism for Boolean Constraint Satisfaction
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
The Isomorphism Problem for Read-Once Branching Programs and Arithmetic Circuits
The Isomorphism Problem for Read-Once Branching Programs and Arithmetic Circuits
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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.