Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
On the Ring Isomorphism and Automorphism Problems
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Automorphisms of finite rings and applications to complexity of problems
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Complexity of Ring Morphism Problems
Computational Complexity
Efficient algorithms for some special cases of the polynomial equivalence problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Affine projections of polynomials: extended abstract
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We study the isomorphism problem of two “natural” algebraic structures – $\mathbb{F}$-algebras and cubic forms. We prove that the $\mathbb{F}$-algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form $3 \Lambda(\#\mathbb{F} - 1)$, this result implies that the two problems are infact equivalent. This result also has the following interesting consequence: Graph Isomorphism ${\leq}^P_m$$\mathbb{F}$-algebra Isomorphism ${\leq}^P_m$ Cubic Form Equivalence.