The previous chapter introduced the Turing machine computation model. Advancing from the simple, single-tape deterministic TM model, we also learned more complex TM models. An important fact is that the simplest model can compute anything these seemingly more powerful variants can, at the cost of some slowdown. In this and the following chapters, we study the use of TMs to detect the properties of other TMs, automata, regular expressions, and context-free grammars.