Recent content by derivador

I think this was the origin of my confusion. I was interpreting it as an unique TM starting with a blank tape, inserting the input itself, computing and halting; all alone. I'm very layman on this subject and started to study it this week for pure curiosity. That's the price of skipping steps...

Yes. I was considering the program as a busy beaver-like TM, which starts with a blank tape and halts. In this case, it's length would change for every ##n##. Sorry for the confusion and thanks for your answer. I got it!

Yes, I think I got it. My example was just to illustrate the essence of the idea. I mean, to compute ##BB(1512)##, for the sake of argument, I would need at least a 3500-length TM which would be the smaller program that computes ##f(1001)## in this case. I'm just talking about the program...

So, it would work only for all ##m < n## with ##n## being the length of the program that computes ##f(1000)##, right? In my example, ##n = 1500##, and I could compute every ##BB(m)## with ##m < 1500##, but not ##BB(1512)## for example. Did I get it right?

Sorry, but I can't understand this implication. Since I can't compute f(1000) with a program with length of 1000, f(1000) steps doesn't seem to say anything about BB(1000) to me. I mean, to compute f(1000) you would need, for the sake of argument, a program with 1500 of length, and to compute...