CSE 555 Theory of Computation (2/28) - Organic Origami

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Turing machine computation

Initially, input w = w 1 , · · · , w k at the left end of the tape.

Initially, rest of tape blank (filled with ⊔).

Initially, tape head at leftmost square.

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Turing Machine Definition A Turing machine is a 7-tuple (Q, Σ, Γ, δ, q 0 , q a , q r ), where Q is a finite set (of states). Σ is a finite set (input alphabet), ⊔ ∉ Γ. Γ is a finite set (tape alphabet), Σ ⊆ Γ and ⊔ ∈ Γ. δ : Q × Γ → Q × Γ × {L, R} is a transition function. q 0 ∈ Q (the start state). q a ∈ Q (the accept state). q r ∈ Q (the reject state).

Turing machine computation Initially, input w = w 1 , · · · , w k at the left end of the tape. Initially, rest of tape blank (filled with ⊔). Initially, tape head at leftmost square.

Page 1 and 2: CSE 555 Theory of Computation (2/28
Page 3: Turing Machine Input: a string over
Page 7 and 8: Turing machine computation Initiall
Page 9 and 10: Turing-recognizability A Turing mac
Page 11 and 12: Decidability Run M with input w: th
Page 13: Examples L 1 = {0 2n | n ≥ 1} L 2

CSE 555 Theory of Computation (2/28) - Organic Origami

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