4 papers
Quantum precomputation: parallelizing cascade circuits and the Moore-Nilsson conjecture is false
Adam Bene Watts, Charles R. Chen, J. William Helton +1
Parallelization is a major challenge in quantum algorithms due to physical constraints like no-cloning. This is vividly illustrated by the conjecture of Moore and Nilsson from thei…
The discrete Laplace asymptotic method and its application to the 3XOR satisfiability problem
Jared A. Hughes, J. William Helton, Peter Schlosser
A standard way to calculate the asymptotic behavior of integrals of the form \int_Wg(x)e^{-nh(x)}dx is the (continuous) Laplace asymptotic method. However, also discrete sums like…
The Satisfiability Threshold for K-XOR Games
Jared A. Hughes, J. William Helton
A -XORGAME system corresponds to a -XORSAT system with the additional restriction that the variables divide uniformly into blocks. This forms a system of equations wi…
Uniform Convergence of an Asymptotic Approximation to Associated Stirling Numbers
E. Rodney Canfield, J. William Helton, Jared A. Hughes
Let be the -associated Stirling numbers of the second kind, the number of ways to partition a set of size into subsets of size at least . For , these…