Just want a bit of clarification on what you mean by S(A,B) in the main puzzle, because you technically didn't specify what you meant by that notation. I guess it just means the sum of the costs of all possible A trees, and all possible B trees. But doesn't the sum we're looking for also include the cost of a single pulse? So technically we're looking for S(A,B)+1, right?
It can't though. It has been detected. It has been analyzed and found to be repeating. The only question is: Did the scientists tell me the length? (Or depth. But we receive it as a string, right?)
Fair point. Maybe the questions are better thought of as analyzing the space of possible signals (as opposed to actual observed ones). We’ll sort of brush aside the questions of how the signals are transmitted and read. Admittedly, the logic of the puzzle is a little strained under the concept of arbitrarily large signals.
Think of it like a tree where a pulse is a leaf node and the modulators are non-leaf nodes (and the order of children nodes matters). So no, a signal can’t be two consecutive pulses. The closest equivalent would be an alpha modulator with two pulse children. Does that help clarify?
Ahh I see. yah, for the purposes of this question, I left it at those two. But the idea is easily extended to more. It doesn’t change the problem much. I just didn’t want to clutter the problem and thought keeping it at 2 would avoid that.
Just want a bit of clarification on what you mean by S(A,B) in the main puzzle, because you technically didn't specify what you meant by that notation. I guess it just means the sum of the costs of all possible A trees, and all possible B trees. But doesn't the sum we're looking for also include the cost of a single pulse? So technically we're looking for S(A,B)+1, right?
you are correct! the single pulse should be included as well
Do we know the length of the repeating fragment?
(If I’m understanding the question correctly) it can have any length. I’m inclined to use the word “depth”though
It can't though. It has been detected. It has been analyzed and found to be repeating. The only question is: Did the scientists tell me the length? (Or depth. But we receive it as a string, right?)
Fair point. Maybe the questions are better thought of as analyzing the space of possible signals (as opposed to actual observed ones). We’ll sort of brush aside the questions of how the signals are transmitted and read. Admittedly, the logic of the puzzle is a little strained under the concept of arbitrarily large signals.
Can a signal simply be 2 pulses, with no other structure? A pulse followed by a pulse.
Think of it like a tree where a pulse is a leaf node and the modulators are non-leaf nodes (and the order of children nodes matters). So no, a signal can’t be two consecutive pulses. The closest equivalent would be an alpha modulator with two pulse children. Does that help clarify?
Yes it does. It's also sort of evasive. Some options for signals are described. But there aren't any others? This and no more?
The examples were just meant to illustrate the construction. the total number of examples is infinite. For example you could have A(•,A(•,A(•, …)))
Yes, but infinitely many signals can be described in a finite way. A signal is a pulse or a phrase. A phrase is A or B. No other options.
Ahh I see. yah, for the purposes of this question, I left it at those two. But the idea is easily extended to more. It doesn’t change the problem much. I just didn’t want to clutter the problem and thought keeping it at 2 would avoid that.