In my last post I started explaining the theory of computation, starting with its central principle: The Church-Turing Thesis. In this post, I’m going to explain several areas of research in computational theory that, as per the Church-Turing Thesis, are based on the realization that all (full featured) computers are equivalent.

**Turing Machines as Simplified Computers**

Since Turing Machines are known to be equivalent in expressive power to modern computers, it turns out this means that Turing Machines can serve as a very simplified version of a modern computer — or any conceivable computer!

This makes Turing Machines quite useful for exploration of the Theory of Computation. Mathematicians have been able to come up with ‘programs’ written for Turing machines and then – because Turing Machines are so simple – come up with consistent ways of how to measure how fast the program runs given any number of inputs. Continue reading