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**Unformatted text preview: **Introduction In this final set of notes we’ll examine a couple of active research areas which may well determine the future of computing. When we think of a computer we think of modern electronic, digital computers. However, the evolution of the computer has been remarkably fast given the history of man and the term has had many other meanings. For centuries, a computer was a person who did calculations for a living. Computing technology has evolved from counting on fingers to a wide variety of mechanical devices (the abacus (still widely used in parts of the world), adding machines, card readers and sorters), then on to electronic computers of the current era (room-sized mainframes to personal computers on desktops or laptops and embedded systems). There is no reason to think that the evolution of computing technology will stop where it currently is, and there is very good reason to believe that it will continue to evolve at the same rate that occurred in the last three or four decades. Computing with DNA and quantum computing are two of the active research areas that may well shape the future of computing in very dramatic fashion. Computing with DNA In 1994 Len Adleman (the A in the RSA public encryption system) showed that an instance of the Hamiltonian path problem in a directed graph with designated start and end vertices, a problem known to be in NP-C (NP-complete) could be solved using DNA. As we have seen from some of our earlier discussions, it seems unlikely that there will be algorithms, in the usual sense, which will solve NP-C problems feasibly (in polynomially bounded time). However, bio-chemical processes work on huge numbers of molecules in parallel, giving the potential for fast solutions. Adleman’s method has evoked an intense area of computing theory research. We’ll look briefly at Adleman’s experiment and even more briefly at the bio-chemical process (I’m neither a chemist nor a biologist) but our ultimate focus will be the algorithmic process to understand the potential and limitations of DNA computing. The Hamiltonian Path Problem The Hamiltonian path problem (hereafter referred to as HP) in a directed graph with designated start and end vertices is a very hard problem to solve for a general directed graph, it is NP-C, so there are no polynomial time solutions to this problem. The input consists of a directed graph G = (V, E), a vertex v start ∈ V, and a vertex v end ∈ V. The decision problem is to determine if there exists a The Possible Future of Computing - 1 The Possible Future of Computing (19) path in G from v start to v end that passes through every other vertex in G exactly once. In many applications, if there is such a path, we would like to find one....

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