Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
?- sum_lengths([],N).
N = 0
Yes
?- sum_lengths([a,akjjdfkpodsaijfospdafpods],N).
N = 26
Yes
Extra credit: The number of characters in a string is not a very good measure of its size, since it matters
whether the elements of the string are taken from a 26 symbol alphabet like {a-z} or a 10 symbol
alphabet like {0-9} or a two symbol alphabet like {0,1}.
The most common size measures are given in terms of two symbol alphabets: we consider how many
symbols are needed for a binary encoding, how many “bits” are needed.
Now suppose that we want to represent a sequence of letters or numbers. Let’s consider sequences of
the digits 0-9 first. A naive idea is this: to code up a number like 52 in binary notation, simply represent
each digit in binary notation. Since 5 is 101 and 2 is 10, we would write 10110 for 52. This is obviously
not a good strategy, since there is no indication of the boundaries between the 5 and the 2. The same
sequence would be the code for 26.
Instead, we could just express 52 in base 2, which happens to be 110100. While this is possible, it is a
rather inefficient code, because there are actually infinitely many binary representations of 52:
110100, 0110100, 00110100, 000110100,,...
Adding any number of preceding zeroes has no effect! A better code would not be so wasteful.
Here is a better idea. We will represent the numbers with binary sequences as follows:
decimal number 0 1 2 3 4 5 6 …
binary sequence ɛ 0 1 00 01 10 11 …
Now here is the prolog exercise:
i. Write a prolog predicate e(N,L) that relates each decimal number N to its binary sequence representation
L.
ii. Write a prolog predicate elength(N,Length) that relates each decimal number N to the length of its
binary sequence representation.
iii. We saw above that the length of the (smallest – no preceding zeroes) binary representation of 52
is 6. Use the definition you just wrote to have prolog compute the length of the binary sequence
encoding for 52.
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