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Chapter and Conference Paper
Polynomial-Time Isomorphism Test of Groups that are Tame Extensions
We give new polynomial-time algorithms for testing isomorphism of a class of groups given by multiplication tables (GpI). Two results (Cannon & Holt, J. Symb. Comput. 2003; Babai, Codenotti & Qiao, ICALP 2012) im...
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Chapter and Conference Paper
An Efficient Quantum Algorithm for Finding Hidden Parabolic Subgroups in the General Linear Group
In the theory of algebraic groups, parabolic subgroups form a crucial building block in the structural studies. In the case of general linear groups over a finite field
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Chapter and Conference Paper
On the Complexity of Trial and Error for Constraint Satisfaction Problems
In a recent work of Bei, Chen and Zhang (STOC 2013), a trial and error model of computing was introduced, and applied to some constraint satisfaction problems. In this model the input is hidden by an oracle wh...
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Chapter and Conference Paper
Determinantal Complexities and Field Extensions
Let \(\mathbb{F}\) be a field of characteristic ≠ 2. The determinantal complexity of a polynomial
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Chapter and Conference Paper
Polynomial-Time Isomorphism Test for Groups with No Abelian Normal Subgroups
We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial n logn bound on the time complexity for the general case has not been impro...
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Chapter and Conference Paper
On the Security of Goldreich’s One-Way Function
Goldreich (ECCC 2000) suggested a simple construction of a candidate one-way function f: {0,1} n → {0,1} m where each bit of output is a fixed...