# week2 - Week 2 Lecture 3 TM tape two way can write…...

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Unformatted text preview: Week 2: Lecture 3 TM : tape: two way, can write… Formally, Turing machine M is a 7-tuple, (Q, Σ , Γ , δ , q0, q accept , q reject ,), where 1. Q is the set of states 2. Σ is the input alphabet not containing the special blank symbol ⊆ 3. Γ is the tape alphabet, where { ⊆ } ∈ Γ and Σ ⊆ Γ 4. δ : Q × Γ → Q × Γ × {L.R} is the transition function (not a mapping) 5. q0 ∈ Q is the initial state 6. q accept ∈ Q is the accept state 7. q reject ∈ Q is the reject state, where qaccept, ≠ qreject Configuration of M: uqv (head is at the first symbol of string v) Start configuration Accepting configuration uaq i bv yields uacq j v if δ (q i ,b) = (q j ,c,R) M accepts w: C1 is the start conf of M on input w Each C i yields C i+1 C k is the accepting conf Note that the definition hold even for a NDTM. Even in this case, we have many variations: determinism vs. non det 1 tape vs. multi tape read only vs. read write Theorem: If an algorithm A has time complexity O(n k ), then there is a TM M which can implement A in O(n...
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week2 - Week 2 Lecture 3 TM tape two way can write…...

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