Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence
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Exercise 9.1
Code the instruction bodies of the solutions to the exercises in chapter eight. (Disregard the line numbers for the moment – just code the instructions.) Now that we know how to code instructions, we are going to use exactly the same procedure to code entire programs. A program is some number n of lines consisting of a line number and an instruction. To simplify things, we make the assumption that lines are numbered in the sequence of natural numbers beginning from 1. When we decode program codes into their constituent instruction codes, we simply enumerate them in the same sequence. This allows us to disregard line numbers in codes. Given a sequence of n instructions, we can code this by simply mul- tiplying the first n primes, each of which is raised to the exponent which is the code of the relevant instruction. So the first prime is raised to the exponent which is the code of the first instruction, the second prime is raised to the exponent which is the code of the second instruction, and so on. To express this symbolically: 90 given a program 1 1 , 2 2 , 3 3 , . . . , n n it can be coded as 2 #1 . 3 #2 . 5 #3 . . . p #n (where p is the nth prime). This might seem rather complicated but some examples will serve to show that it is actually very straightforward. We always simply leave the expressions in their exponential form and we assign variables to stand for instruction codes to make things easier to read, as the exam- ples below illustrate. The program: 1 D 3 1 2 2 D 1 3 5 3 D 2 4 5 4 I 3 2 is coded as: 2 a . 3 b . 5 c . 7 d where: a 3 . 5 3 . 7 1 . 11 2 b 3 . 5 1 . 7 3 . 11 5 c 3 . 5 2 . 7 4 . 11 5 d 2 . 5 3 . 7 2 The program: 1 D 3 1 2 2 D 4 2 3 3 D 1 4 9 4 D 2 5 7 5 I 3 6 6 I 4 4 7 D 4 8 3 8 I 2 7 9 D 3 10 12 10 I 1 9 is coded as: 2 a . 3 b . 5 c . 7 d . 11 e . 13 f 17 g . 19 h . 23 i . 29 j where: a 3 . 5 3 . 7 1 . 11 2 b 3 . 5 4 . 7 2 . 11 3 c 3 . 5 1 . 7 4 . 11 9 91 d 3 . 5 2 . 7 5 . 11 7 e 2 . 5 3 . 7 6 f 2 . 5 4 . 7 4 g 3 . 5 4 . 7 8 . 11 3 h 2 . 5 2 . 7 7 i 3 . 5 3 . 7 10 . 11 12 j 2 . 5 1 . 7 9 Download 1.05 Mb. Do'stlaringiz bilan baham: |
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