Abstract
This paper postulates a novel N-dimension computing machine that operates in an unconventional manner. This postulate aims at solving existing problems in higher dimensions, where one must re-think the scope of a given problem domain beyond the one-dimension Turing machine to dictate all subsequent problem representation, problem transformation, and algorithmic derivation. Two over-simplified well-known problems, namely, the Traveling Salesman Problem and the Tower of Hanoi problem are presented to demonstrate the point. Both synthetic problems are effectively adapted to solve a real world project. To realize the postulate in a viable architectural construct, data flow and molecular computers are investigated since they show potential computation power. Unfortunately, they are still confined to working in one-dimension domain. A biological-like architecture for software systems is proposed in three design aspects: structure, function, and behavior. Contributions of this work are to revamp traditional Turing computation paradigm to N-dimension computing machine, yet it is simple, straightforward, and implementable by state-of-the-practice hardware and software technologies. Thus, the burden of solving difficult problems can be lessened.
Highlights
The advent of electronic computers has revolutionized myriad of problem solving venues to a new realm of computation
Since all factors could be simultaneously mapped onto their corresponding values in the problem space and fired concurrently, the answer to the Traveling Salesman Problem (TSP) might be near optimal which could be computed in shorter time than working in the 1-D computing space
Such a claim will be further investigated in the proposed N-dimension computing machine postulate
Summary
The advent of electronic computers has revolutionized myriad of problem solving venues to a new realm of computation. What was previously solved analytically is carried out numerically with the help of algorithms so developed Such an undertaking is equivalent to transforming the original problem from one domain to another domain which is known as the ‘‘mapping’’ process. For molecular or DNA manipulations, Adleman estimates 1020 operations per second [13] Such a considerable improvement still does not solve the second aspect in that it merely speeds up the computations, yet leaves the number of steps to solve the problem unconsidered. The N-to-1 problem to Turing machine transformation and the 1-to-N solution to problem might not losslessly project back to the original problem domain This is the essence complexity which is the main focus of this work to transform the problem to solution in an N-to-N fashion and to accomplish the second aspect.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
