Abstract:
In [12] a probabilistic solution to the Infinite Merchant’s Problem, an undecidable
problem equivalent to the Halting Problem, was proposed. The solution uses a real
Hilbert space and is based on the estimation of the exponential growth of an unbounded
semigroup. The aim of this paper is to offer an alternative solution in terms of scattering
processes on quantum dots. We will reduce the problem to a special scattering problem,
observe the results of multiple acts of scattering and, finally, estimate the deviation of
the scattered data from the input data.
