The Turing Machine

By: Hayden Muditajaya

A Turing Machine invented by Alan Turing in 1936, is a mathematical model which can compute mathematical problems through inputs and outputs. It takes a memory tape storing symbols as input and reads each node with a read-write head. There can be a given rules to the machine which can affect the way the memory tape is read or how it writes the information down. An example of this machine would be Boolean values; the memory tape consists of 1s and 0s while 1 represents true and 0 represents false. The tape will output true and false based on the values shown on the tape. There are also states within the Turing machine. Having a different state can affect the output for same values. If the machine outputted 1 as true and then the state was flipped, the machine could output 1 as false. As output, the machine will use the read-write head to write on the memory tape. Dependent on the state of the machine, the machine can overwrite values on the memory tape. What is most effective of this machine is that it is “Turing complete”. This means that theoretically, this machine is able to compute any algorithm. Another benefit of Turing machines is that they are not limited to their hardware. There are no constraints on the memory tape or constraints on how many symbols and outputs there are.

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The Turing Machine is essentially the most influential piece of technology to this day. The Turing Machine influenced society as because it can solve any equation, every modern device utilizes a Turing machine. The term “Turing complete” is used to describe a computer which is possible to compute anything. All modern devices and computers to this day are all “Turing complete”.  However, one problem with the computer is the “Halting Problem”. The halting problem is a theory which questions given a computer program, if the program will finish executing or run indefinitely. This is the only problem which the Turing machine cannot complete.

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My computational artifact is a model of the Turing machine. The list, memoryTape, represents the memory tape in the machine. It consists of the symbols 1 and 0. It uses a loop which loops the entire list. There are 2 cases for the list since there are 2 variants within the memory tape. Having the symbol 1 represents true while having the symbol 0 represents false.

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In order to create my process, I first started off by replicating the memory list. Nothing more represented that storage of memory than an array. Then, I created an iterating loop which executes as many items are in the memory list. Finally, I created a switch statement which will execute the outcome for the number of different symbols in the list.

https://link.springer.com/chapter/10.1007/978-3-642-29952-0_1#:~:text=It%20helped%20led%20to%20asymptotic,computation%20and%20a%20valid%20computation. Author: John Hopcroft. Title: On the Impact of Turing Machines. Accessed: 5/24/2022

Alan Turing: Crash Course Computer Science #15

 Author: Crash Course. Title: Alan Turing: Crash Course Computer Science #15. Accessed: 5/24/2022