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A non-deterministic Turing machine is a theoretical type of computer in which specific commands may allow for a range of actions, rather than a specific command leading to only one allowable action in the deterministic model of computing.
Where deterministic programming is a simple condition of ‘input X leads to action Y’, a non-deterministic Turing machine setup would theoretically allow for input X to lead to a variety of actions Y(array).
Non-deterministic Turing machines could really provide a direction for the future of smart or artificially intelligent computing. By untethering computational work from the deterministic paradigm, computers could learn to solve more complicated problems and ‘think’ more like humans.
One type of non-deterministic Turing machine is the probabilistic Turing machine. Here, the array of actions (Y) spoken of above is determined through some probability distribution. Another way to say this is that when the machine has more than one choice, it goes to a probabilistic model, analyzes that model, and makes a choice accordingly.
There are many other ways to order a non-deterministic Turing machine, but the principle is that the computer has to choose from an available set of options. Some non-deterministic Turing models in a machine learning setup might consist of the computer following paths of logic to an accepted or rejected end, and then going back and choosing an action accordingly.
As experts point out, non-deterministic Turing machines are different than quantum computing models. In quantum computing, the confluence of binary bits into qubits broadens the paradigm and makes the computing processes more elaborate and sophisticated.
In the non-deterministic Turing machine, as explained, it's the availability of choices according to inputs that takes the computing model away from pure determinism.