CSC 360 Turing Machines as Language Acceptors

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CSC 360 Turing Machinesas Language Acceptors

• Dr. Curry Guinn

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Todays Class

• Hand back midterm 2
• 1 problem from the Homework due today
• A Turing machine that turns w into wr
• Turing Machines as Language Acceptors
• Acceptance by Final State
• Acceptance by halting (Section 8.3)

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1 problem from homework

• 17 b, c, d, e
• 18 a-c

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A TM that changes w to wr

• http//ironphoenix.org/tril/tm/

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Acceptance by Final State

• A Turing machine is a quintuple
• M (Q, S, ?, ?, q0, F) where
• Q is a finite set of states,
• ? is a finite set called the tape alphabet,
• ? contains a special symbol B that represents a
  blank,
• S is a subset of (? - B) called the input
  alphabet,
• ? is a partial function from Q x ? to Q x ? x
  L,R called the transition function,
• q0 ? Q is a distinguished state called the start
  state, and
• F ? Q
• A string is accepted by M if it halts in a final
  state.
• L(M) is the set of all strings accepted by M.

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Acceptance by TM

• Build a TM that accepts anbn.

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Acceptance by Halting

• A Turing machine is a quintuple
• M (Q, S, ?, ?, q0) where
• Q is a finite set of states,
• ? is a finite set called the tape alphabet,
• ? contains a special symbol B that represents a
  blank,
• S is a subset of (? - B) called the input
  alphabet,
• ? is a partial function from Q x ? to Q x ? x
  L,R called the transition function, and
• q0 ? Q is a distinguished state called the start
  state.
• A string is accepted by M if it halts.
• L(M) is the set of all strings accepted by M.

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For Next Class, Tuesday

• Tuesday
• Two track machines (Section 8.4)
• Two way machines (Section 8.5)
• Thursday
• Gödel, Escher, Bach Chapter XVIII Artificial
  Intelligence Retrospects
• Quiz