The BKO:

sa: context bigger binary tree sa: child |*> #=> left |_self> + right |_self> sa: left-op |*> #=> merge-labels(|_self> + |0>) sa: right-op |*> #=> merge-labels(|_self> + |1>) sa: left |x> => |0> sa: right |x> => |1> sa: left |0> => |00> sa: right |0> => |01> sa: left |1> => |10> sa: right |1> => |11>That gives us a seed tree, now we can grow it rapidly. First note the results of applying child^k to |x>:

sa: child |x> |0> + |1> sa: child^2 |x> |00> + |01> + |10> + |11>Now, we use this to grow the tree!

map[left-op,left] child^2 |x> map[right-op,right] child^2 |x> map[left-op,left] child^3 |x> map[right-op,right] child^3 |x> map[left-op,left] child^4 |x> map[right-op,right] child^4 |x> map[left-op,left] child^5 |x> map[right-op,right] child^5 |x> map[left-op,left] child^6 |x> map[right-op,right] child^6 |x>And now we are done. And it is trivial to make even bigger trees using the same method.

Here is the result:

sa: dump ---------------------------------------- |context> => |context: bigger binary tree> child |*> #=> left |_self> + right |_self> left-op |*> #=> merge-labels(|0> + |_self>) right-op |*> #=> merge-labels(|1> + |_self>) child |*> #=> left |_self> + right |_self> left-op |*> #=> merge-labels(|_self> + |0>) right-op |*> #=> merge-labels(|_self> + |1>) left |x> => |0> right |x> => |1> left |0> => |00> right |0> => |01> left |1> => |10> right |1> => |11> left |00> => |000> right |00> => |001> left |01> => |010> right |01> => |011> left |10> => |100> right |10> => |101> left |11> => |110> right |11> => |111> left |000> => |0000> right |000> => |0001> left |001> => |0010> right |001> => |0011> left |010> => |0100> right |010> => |0101> left |011> => |0110> right |011> => |0111> left |100> => |1000> right |100> => |1001> left |101> => |1010> right |101> => |1011> left |110> => |1100> right |110> => |1101> left |111> => |1110> right |111> => |1111> left |0000> => |00000> right |0000> => |00001> left |0001> => |00010> right |0001> => |00011> left |0010> => |00100> right |0010> => |00101> left |0011> => |00110> right |0011> => |00111> left |0100> => |01000> right |0100> => |01001> left |0101> => |01010> right |0101> => |01011> left |0110> => |01100> right |0110> => |01101> ...And here is the picture:

## No comments:

## Post a Comment