Lower bounds on the complexity of the wavelength-based machine

• Authors: Sama Goliaei;Mohammad-Hadi Foroughmand-Araabi
• Venue: UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
• Year: 2012

The optical wavelength-based machine, or simply w-machine, is a computational model designed based on physical properties of light. The machine deals with sets of binary numbers, and performs computation using four defined basic operations. The sets are implemented as light rays and wavelengths are considered as binary numbers. Basic operations are then implemented using simple optical devices. In this paper, we have provided a polynomial lower bound on the complexity of any w-machine computing all satisfiable SAT formulas. We have shown that the provided lower bound is tight by providing such a w-machine. Although the size complexity of the SAT problem on w-machine is polynomial, but, according to the provided optical implementation, it requires exponential amount of energy to be computed. We have also provided an exponential lower bound on the complexity of most of w-machine languages, by showing that when n tends to infinity, the ratio of n-bit languages requiring exponential size w-machine to be computed, to the number of all n-bit languages, converges to 1.