Abstract
The simple universal Turing machine designed to work with the Game of Life Turing machine contains a description of the target Turing machine in the form of a list of transitions. It will work with the transitions in any order. However the order makes is a great deal of difference to the size of the list on the universal Turing machine’s tape and the speed of operation. It was considered worth trying to minimise the size of the coded transition list for the unary multiplication Turing machine in order to minimize the size of the stacks required and therefore the size of the Game of Life pattern needed to run it. This optimisation is described in this chapter. It was found to be a quadratic assignment problem. A surprisingly simple procedure was found be successful in solving this simple example. The SUTM will work with the transitions in any order. However the order makes is a great deal of difference to the size of the list on the UTM tape and the speed of operation. It was considered worth trying to minimise the size of the coded transition list for the unary multiplication TM in order to minimize the size of the stacks required and therefore the size of the GoL pattern shown in Fig. 5.20.
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Rendell, P. (2016). Optimizing Transition Order. In: Turing Machine Universality of the Game of Life. Emergence, Complexity and Computation, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-19842-2_6
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DOI: https://doi.org/10.1007/978-3-319-19842-2_6
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