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Turing Machine Variants

Explore variations such as multitape, nondeterministic, and enumerators in Turing machines. Learn how they redefine functions and their equivalence to single-tape machines. Understand the concept of Turing-recognizable languages through an enumerator.

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Turing Machine Variants

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  1. [Section 3.2] Variants of Turing Machines • what if a TM has more tapes ? several heads ? • This section: we’ll give detailed descriptions of our machines but not give detailed ±-functions.

  2. [Section 3.2] Multitape Turing Machines • have to redefine ±-function: • Thm 3.13: Every multitape TM has an equiv. single-tape TM.

  3. [Section 3.2] Nondeterministic Turing Machines • have to redefine ±-function: • Thm 3.16: Every nondeterministic TM has an equivalent deterministic TM.

  4. [Section 3.2] Enumerators An alternative name for Turing-recognizable languages is recursively enumerable languages. An enumerator is a TM-like “printer” with no input and an extra output tape that prints all strings in a given language.

  5. [Section 3.2] Enumerators Thm 3.21: A language is Turing-recognizable iff there is an enumerator for it.

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