(3) A possible solution derived by Copycat to the problem abc : abd, xyz : ? is wyz. This solution is driven by the fact that a is the first letter in the alphabet and z is the last, allowing a correspondence to be formed between them. For the solution wyz to be formed in the Workspace:

[1 mark]

(a) what would be the initial and modified rule that allows this to occur ?

initial rule: replace ________________________ by __________________________

modified rule: replace ________________________ by __________________________

[1 mark]

(b) The slippages between the concepts used in the initial and modified rule are either implied by or incorporated in the correspondence that is built between the groups abc and xyz. Denote what descriptions would be attached to the two groups, the slippages that occur when the two groups are mapped, and what implied slippages are required to derive the modified from the initial rule above.

Implied conceptual slippage

(c)

[1 mark]

In the following diagram fill in the descriptions attached to the letters, the bonds that from between the letters, and the correspondences between letters that are consistent with your answer to (b) above.

first

last

(4)

[0.5 marks]

What is the effect of clamping the temperature

(a) at a high value (i.e. 100)

[0.5 marks]

(b) at a low value (i.e. 10)

[1 mark]

(c) As the temperature falls from a high to a low value during the formation of a solution, what do your answers to (a) and (b) imply about the search strategy employed by Copycat.

EXAM SOLUTIONS

(3) A possible solution derived by Copycat to the problem abc : abd, xyz : ? is wyz. This solution is driven by the fact that a is the first letter in the alphabet and z is the last, allowing a correspondence to be formed between them. For the solution wyz to be formed in the Workspace:

[1 mark]

(a) what would be the initial and modified rule that allows this to occur ?

initial rule: replace (letter category of) rightmost letter by successor

modified rule: replace (letter category of) leftmost letter by predecessor

note: I have included “letter category of” in braces as I think this should be optional information and there may not be room to write it in the space provided.

[1 mark]

(b) The slippages between the concepts used in the initial and modified rule are either implied by or incorporated in the correspondence that is built between the groups abc and xyz. Denote what descriptions would be attached to the two groups, the slippages that occur when the two groups are mapped, and what implied slippages are required to derive the modified from the initial rule above.

Actual slippages: successor -> predecessor, right -> left

Implied slippage: rightmost -> leftmost

Note: there are actually 2 ways in which this problem can be solved. The second solution involves “abc” being perceived as a left-going predecessor group with “xyz” being a right-going successor group. In this case the actual slippages will be reversed, and the implied slippages “successor->predecessor” and “right->left” would need to be added before “rightmost -> leftmost” can be inferred. The direction of the bonds etc, will need to be reversed in the following questions if this solution is given.

(c)

[1 mark]

In the following diagram fill in the descriptions attached to the letters, the bonds that from between the letters, and the correspondences between letters that are consistent with your answer to (b) above.

last

(1) What is the effect of clamping the temperature

(a) at a high value (i.e. 100)

* many responses are possible, many of them not so good solutions

(b) at a low value (i.e. 10)

* only a few different solutions are possible, which are the most obvious ones. Note: I say the most obvious, not the best. Some solutions such as “ulleeee” to “abc:abd, ulleee:?” are the best solutions as far as final temperature goes, but will not be found if temperature is clamped at this low level.

(c) As the temperature falls from a high to a low value during the formation of a solution, what do your answers to (a) and (b) imply about the search strategy employed by Copycat.

During a run, many alternatives are explored initially (i.e. a wide net is cast), with the search being narrowed to the best possible solutions over time.