Fluoroantimonic Acid asked whether there is a busy beaver function for channel systems. I tentatively propose the following. Let the length of an LCS be its alphabet size + number of channels + number of states. Let L be a single-agent LCS such that a maximal simulation of L from an initial configuration with empty channels ends with L halting, and call the sum of the sizes of the channels its output. Let M(L) be the maximal output of L (undefined if its outputs can become arbitrarily large). Then \(\Sigma_\text{LCS}(n)\) is the maximal possible value of M(L) given that L has length at most n.

I don't know if this is googological. -- vel! 19:12, September 3, 2015 (UTC)

I realize that this relies on boundedness so it's not computable :( -- vel! 17:17, September 20, 2015 (UTC)

"A simulation is maximal iff it goes on infinitely or halts." Is there a simulation which does not halt and not go on infinitely? Maybe called Googology Noob (talk) 05:51, January 27, 2016 (UTC)

The thing is, according to definitions from this article, a simulation is any sequence of consecutive steps, not necessarily the one which we continue as long as we can. So for an example, take any non-halting system and simulate it for 7 steps. This will be a non-maximal simulation. LittlePeng9 (talk) 15:06, January 27, 2016 (UTC)
OK, I understand. Thanks! Maybe called Googology Noob (talk) 05:40, January 28, 2016 (UTC)