1210.3304 (Aran Nayebi)

Plausible hypercomputability    [PDF]

Aran Nayebi

For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of \emph{any} information-processing machine that computes beyond the universal Turing machine. To this end, I present a more mathematically concrete challenge to hypercomputability, and will show that one is immediately led into physical impossibilities, thereby demonstrating the infeasibility of hypercomputers more generally. This gives impetus to propose and justify a new direction that hypercomputability should take in order to be physically possible, at least in principle. Instead of attempting to rely on infinities such as idealized limits of infinite time or numerical precision, or some other physically unattainable source, the field should be geared toward extending the classical paradigm to better encapsulate modern computational problems that are not well-expressed/modeled by the closed-system paradigm of the Turing machine. I present the first steps toward this goal by considering contemporary computational problems dealing with intractability and issues surrounding cyber-physical systems, and argue that a "plausible hypercomputability" should focus on these issues in order to be practically viable.

View original: http://arxiv.org/abs/1210.3304