As generalização das máquinas de turing por meio dos grafos cayley na solução de problemas não recursivamente enumeráveis

Abstract

Long before digital computers are developed, Alan M. Turing proposed a machine with the same computational power of current machines, Turing machines, a model able to represent any computable function. This model consisted of one-dimensional tapes. However, despite all presented efficiency, traditional machines can not compute some problems that call undecidable. Undecidable problems are problems that can not be computed by any existing algorithm. So, since the restraining power of traditional machines, new models have been proposed. Then came the geometry of interest with backup tapes, which improved the outcome of these machines. It also emerged machines modeled with two-dimensional graphs, Cayley graphs considered, representing a major advance in its computational power. This new model showed significant advance in computing problems undecidable, since Turing machines with Cayley graphs show is strictly more powerful than traditional machines.