chapter 12Computational Notions

Give us the tools, and we will finish the job.

—Winston Churchill (1874–1965). © Winston Churchill from speech broadcasted on February 9th, 1941.

Is there a computing device more powerful than any other computing device? What does “powerful” mean? Can we easily compare machines to see whether they have the same power? We’ll try to answer these questions by studying Turing machines and the Church-Turing thesis, which claims that there are no models of computation more powerful than Turing machines.

Some problems can’t be solved by any machine; moreover, some problems that can be solved might be impractical because they take too much time or space. We’ll discuss the limits of computation, noting some classic problems ...

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