Mathematical Software – ICMS 2018

s of Invited Talks Short of Proof: How Many Digits are Nonetheless Correct?

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[9]  O. Regev.  A Subexponential Time Algorithm for the Dihedral Hidden Subgroup Problem with Polynomial Space , 2004, quant-ph/0406151.

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[11]  Greg Kuperberg.  A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem , 2005, SIAM J. Comput..

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[14]  Alexander Russell,et al.  Normal subgroup reconstruction and quantum computation using group representations , 2000, STOC '00.

[15]  Umesh V. Vazirani,et al.  Quantum mechanical algorithms for the nonabelian hidden subgroup problem , 2001, STOC '01.

[16]  Gábor Ivanyos,et al.  Quantum computation of discrete logarithms in semigroups , 2013, J. Math. Cryptol..

[17]  Rekha R. Thomas,et al.  Computing Gröbner fans , 2007, Math. Comput..

[18]  Akira Suzuki,et al.  A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases , 2006, ISSAC '06.

[19]  Emanuel Knill,et al.  The quantum query complexity of the hidden subgroup problem is polynomial , 2004, Inf. Process. Lett..

[20]  Volker Weispfenning.  Constructing Universal Groebner Bases , 1987, AAECC.

[21]  George Petrides.  Cryptanalysis of the Public Key Cryptosystem Based on the Word Problem on the Grigorchuk Groups , 2003, IMACC.

[22]  Aleks Kissinger,et al.  Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem , 2017, 1701.08669.

[23]  Komei Fukuda,et al.  The generic Gröbner walk , 2007, J. Symb. Comput..

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[25]  Renato Portugal,et al.  An Efficient Quantum Algorithm for the Hidden Subgroup Problem over some Non-Abelian Groups , 2015 .

[26]  Dmitry Gavinsky,et al.  Quantum solution to the hidden subgroup problem for poly-near-hamiltonian groups , 2004, Quantum Inf. Comput..

[27]  Alexander Russell,et al.  Quantum-Secure Symmetric-Key Cryptography Based on Hidden Shifts , 2016, EUROCRYPT.

[28]  Dima Grigoriev,et al.  Testing Shift-Equivalence of Polynomials by Deterministic, Probabilistic and Quantum Machines , 1997, Theor. Comput. Sci..

[29]  T. Beth,et al.  Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups , 1998, quant-ph/9812070.

[30]  R. Portugal,et al.  Solution to the Hidden Subgroup Problem for a Class of Noncommutative Groups , 2011, 1104.1361.

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[32]  Gilles Brassard,et al.  An exact quantum polynomial-time algorithm for Simon's problem , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[33]  Amir Hashemi,et al.  Gröbner Systems Conversion , 2017, Mathematics in Computer Science.

[34]  Frédéric Magniez,et al.  Efficient Quantum Algorithms For Some Instances Of The Non-Abelian Hidden Subgroup Problem , 2003, Int. J. Found. Comput. Sci..

[35]  Yao Sun,et al.  A new algorithm for computing comprehensive Gröbner systems , 2010, ISSAC.

[36]  F. Gall,et al.  An Efficient Algorithm for the Hidden Subgroup Problem over a Class of Semi-direct Product Groups , 2004 .

[37]  Frédéric Magniez,et al.  Hidden translation and orbit coset in quantum computing , 2002, STOC '03.

[38]  Alan Veliz-Cuba,et al.  The Neural Ring: An Algebraic Tool for Analyzing the Intrinsic Structure of Neural Codes , 2012, Bulletin of Mathematical Biology.

[39]  Oded Regev.  Quantum Computation and Lattice Problems , 2004, SIAM J. Comput..

[40]  J. O'Keefe,et al.  The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. , 1971, Brain research.