Turing Machines:

• The Structure of Turing machines
• Deterministic Turing machines represented by DTM

- Accepting a language

- Computing a function

• Composite Turing machines
• Multitape Turing machines
• Nondeterministic Turing machines represented by NTM
• Universal Turing machines represented by UTM

• Determine if an input x is in a Determine if an input x is in a language.

- That is, answer if the answer of a problem P for the instance x is "yes".

• Compute a function

- Given an input x, what is f(x)?

- language.

- That is, answer if the answer of a problem P for the instance x is "yes".

• Compute a function

-Given an input x, what is the value for f(x)?

Working of turing machine:

• In the beginning,

- ATM is in theinitial state

- its tape head points at the 1st cell

- The tape contains D, following by input string, and rest of the tape contains D.

• For each move, a TM

——读取波形的象征r its tape head

- In accordanve to thetransition functionon the symbol read from tape and its current state, the TM:

• write down the symbol on tape
• move its tape head to the left or right one cell or not
• changes its state tonext state

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