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Page 1: Artificial Intelligence CS 441/541

Artificial IntelligenceCS 441/541

Instructor: Melanie Mitchell

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Harold Cohen and AARON

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Proof of undecidability of the halting problem:

(1) Define h (g, i): = 1 if g halts on i, 0 otherwise. Assume h exists.

(2) Define h’(g) = returns 1 if h(g,g) returns 0; goes into infinite loop otherwise.

Does h’(h’) halt?

h’(h’) halts iff h(h’,h’) returns 0, which, by (1), implies h’ does not halt on h’.

h’(h’) does not halt iff h(h’,h’) returns 1, which, by (1), implies h’ does halt on h’. CONTRADICTION!

Therefore, h cannot exist.

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Story: “John went to a restaurant. The hostess seated John. The hostess gave John a menu. The waiter came to the table. John ordered lobster. John was served quickly. John left a large tip. John left the restaurant.”

Questions for SAM and SAM’s answers:

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Restaurant script:

• roles customer C, waiter W

• props table T, menu M, food F, bill B, money D

• settings restaurant R

• entry conditions C is hungry, C has D

• results C is satiated

• scenes

• 1. Entering: C goes to R, C sits at T

• 2. Ordering: C reads M, C chooses F, W comes to T, C requests F from W

• 3. Eating: W brings F to C, C eats F

• 4. Exiting: W brings B to C, C gives D to W, C leaves R

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