What the heck is a Turing Machine?
This unique invention led to modern computing.
A Turing machine is a simple “computer” that can perform mathematical operations. It has a tape that runs through it, and the tape is divided into squares. Each square can hold a symbol like a number or a letter.
The machine has a "head" that can read the symbols on the tape and move left or right. It also has a set of rules that tell it what to do based on the symbol it's currently reading and its current state.
For example, let's say the machine starts with the number "5" on the first square of the tape. The machine might have a rule that says "if you see a 5, change it to a 6 and move the head one square to the right." So the machine would change the 5 to a 6 and move the head to the next square.
Turing machines are important in computer science because they are the foundation of modern computing. They provide a model of computation that can be used to analyze algorithms and determine their efficiency and effectiveness. They help us understand what computers can and cannot do, and they are the basis for many computer languages and programming concepts.
The significance of the Turing machine in computer science lies in its ability to perform any computation that is algorithmically solvable (this means we can use a Turing machine to assess if a certain problem can be solved with a computer at all!!). This concept, known as the Church-Turing thesis, is the foundation of the theory of computation. At its heart, the Turing machine helps us understand the limits of what computers can and cannot do.
The Turing machine was first proposed by the British mathematician Alan Turing in 1936, as a way to formally define the concept of an effective procedure or algorithm. His work laid the foundation for the development of modern computers and has had a profound impact on the field of computer science. The Turing machine is still widely studied and used as a theoretical tool to understand the capabilities and limitations of computers and algorithms.
Turing Machine Example (for those interested)
Let me walk you through a step-by-step explanation of how a Turing machine solving a simple problem such as deciding whether an input string is a palindrome or not (a palindrome is a word that is read the same forwards as it is backwards like “radar”).
The machine is in its start state and the tape contains the input string, let's say "radar".
The machine reads the first symbol on the tape, which is "r", and compares it to the last symbol on the tape, which is also "r".
Since the first and last symbols match, the machine moves the tape one symbol to the right and one symbol to the left, respectively.
The machine now reads the next symbols on the tape: "a" and "a", and again compares them.
The machine continues this process of reading, comparing and moving the tape until it reaches the middle of the tape.
If all the symbols on the tape match from left to right and from right to left, the machine enters into accept state, indicating that the input is a palindrome.
If at any point the symbols do not match, the machine enters into reject state indicating that the input is not a palindrome.
The machine stops at this point.
It's worth noting that the above steps are just a simple example of how a Turing machine could solve a problem, the machine could be programmed to follow different set of rules and different states to solve more complex problems.
Turing machines are a tough topic to teach…and I will be continuing to work on how I present this material to students in the future, so we’d love your feedback on this article.
— Steve
ps: I am now offering private coding lessons on Fiverr (this will primarily help me learn more about the needs of learners following The Nestomir journey)