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Turing Machines and Computability

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  • Are Turing machines computable?

    Turing machines can compute any function normally considered computable; in fact, it is quite reasonable to de ne computable to mean computable by a TM. TMs were invented in the 1930s, long before real computers appeared. They came at a time when mathemati-cians were trying to come to grips with the notion of e ective computation.

  • What are some examples of Turing computability?

    The textbooks of Davis (1958) and Minsky (1967) did more. Nowadays Turing computability is often reformulated (e.g. in terms of ‘register machines’). However, computer simulations (e.g., Turing's World , from Stanford) have brought Turing's original imagery to life.

  • What is the determinacy condition of a Turing machine?

    This is the so-calleddeterminacy condition(Section 3). These a-machines are contrasted with the so-called choicemachines for which the next state depends on the decision of anexternal device or operator (Turing 1936–7: 232). A Turingmachine is capable of three types of action:


1 De nition of a Turing machine
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