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What is a Turing Machine?
The concept of Turing machines is fundamental to our understanding of computers and programming. It was invented by Alan Turing in 1936, and illustrates a model of a simple abstract computer (GeeksForGeeks, 2016).
(Chavan & Jadhav, 2023)
Why are Turing Machines important?
Alan Turing is considered one of the founding fathers of Computer Science, and his Turing machine was one such idea that helped shape the development of the subject.
The Turing machine forms the basis of the concept of a Universal Turing Machine, which can do what every Turing machine can do. The Universal Turing Machine is able to understand the program of another machine and mimic its behavior (De Mol, 2018). This develops into the idea of programmable machines, not unlike the computers we use today, which can execute a set of instructions from a program.
Turing machines also serve as a benchmark for Turing-completeness, which is used to evaluate systems and programming languages for their ability to simulate a Turing machine.
Hence, Turing machines and Universal Turing Machines form the conceptual basis of the computers we use today, making it an instrumental part of Computer Science and the theory of Automata.
How does a Turing Machine work?
A Turing machine is essentially a theoretical machine that can manipulate data according to predefined instructions. This data comes in the form of an infinitely long tape divided into squares, with each square containing a symbol. The machine, at any given moment, scans one square and prints a symbol onto it (De Mol, 2018).
The behavior of the machine is affected by a finite state machine, which is a set of states that determine the next action to be taken based on the current state and symbol being read.
The machine will change states, read and write a symbol on the tape, and move to a new square on the tape until an end state is reached, in which case the computation is either accepted or rejected. If the end state reached is an accept state, it is accepted, otherwise it is rejected.
A Turing Machine is formally expressed as a 7-tuple:
(Q, T, B, ∑, δ, q0, F)
Where:
Q represents the set of states;
T represents the symbols that can be written on the tape;
B represents the blank symbol, which is initially printed on the squares on the tape;
∑ (Sigma) represents the symbols in the input alphabet;
δ (Delta) represents a transition function, which changes the machine to a new state;
q0 represents the initial state of the machine,
and F represents the set final states (GeeksForGeeks, 2016).
While this seems like a string of complicated symbols, this essentially defines what the Turing machine does and what data it has to work with.
Conclusion
Mathematically, Turing machines can appear very complex and confusing. However, one does not need to dive into the specifics to understand how important they are in Computer Science.
Reference List
Chavan, P.V. and Jadhav, A. (2023). Turing machine. Automata Theory and Formal Languages, pp.159–179. doi:https://doi.org/10.1016/b978-0-32-391784-1.00015-3.
De Mol, L. (2018). Turing Machines (Stanford Encyclopedia of Philosophy). [online] Stanford.edu. Available at: https://plato.stanford.edu/entries/turing-machine/ [Accessed 31 Jan. 2025].
GeeksforGeeks (2016). Turing Machine in TOC. [online] GeeksforGeeks. Available at: https://www.geeksforgeeks.org/turing-machine-in-toc/ [Accessed 31 Jan. 2025].
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