Turing Machines

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Section 3.1
Turing Machines

• more powerful than PDAs
• what could it have ?

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Section 3.1
Turing Machines
Example A aibici i 0
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Section 3.1
Turing Machines
Example B ww w 2 0,1
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Section 3.1
Turing Machines

• Def 3.3
• A Turing machine (TM) is a 7-tuple
  (Q,,,,q0,qaccept,qreject), where
• Q is the (finite) set of states
• is the (finite) input alphabet, not containing
  ?
• is the (finite) tape alphabet, ? µ
• 
  is the transition function
• q0 2 Q
• qaccept 2 Q is the accept state
• qreject 2 Q-qaccept is the reject state

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Section 3.1
Turing Machines

• Computation of Turing machines
• first we define a configuration
• uqv means the tape contains uv, the state is
  q, and the machine reads the first symbol of v
• suppose configuration is uaqbv and
  (q,b)(p,c,R)
• We say that uaqbv yields

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Section 3.1
Turing Machines

• Computation of Turing machines
• first we define a configuration
• uqv means the tape contains uv, the state is
  q, and the machine reads the first symbol of v
• start configuration
• accepting configuration
• rejecting configuration
• Note accepting/rejecting configurations are
  halting

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Section 3.1
Turing Machines

• Computation of Turing machines
• first we define a configuration
• uqv means the tape contains uv, the state is
  q, and the machine reads the first symbol of v
• A TM M accepts w if
• The language of a TM M is the set of strings that
  M accepts/recognizes.

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Section 3.1
Turing Machines
Def 3.5 A language is Turing-recognizable if
there is some TM that recognizes it. Def 3.6 A
language is Turing-decidable if there is some TM
that decides it.
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Section 3.1
Turing Machines
Example A 0n n2k for some k 0