The model is extremely simple, but has been proven to be able to solve all the problems that any reasonable computer model can solve, thus its adoption as the "default model".
The smallest known Turing machine that cannot be proven to halt or not as of 2019 is 7,918-states: www.scottaaronson.com/blog/?p=2725. Shtetl-Optimized by Scott Aaronson is just the best website.
A bunch of non-reasonable-looking computers have also been proven to be Turing complete for fun, e.g. Magic: The Gathering.
A Turing machine that simulates another Turing machine/input pair that has been encoded as a string.
The concept is fundamental to state several key results in computer science, notably the halting problem.
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A Turing machine is a theoretical computational model introduced by the mathematician and logician Alan Turing in 1936. It is a fundamental concept in computer science and is used to understand the limits of what can be computed. A Turing machine consists of the following components: 1. **Tape**: An infinite tape that serves as the machine's memory. The tape is divided into discrete cells, each of which can hold a symbol from a finite alphabet.