# Busy Beaver

1. Dec 7, 2006

### CRGreathouse

I was trying to find a non-trivial lower bound on the busy beaver ($\Sigma$) function, but I haven't been able to find the function I want. A result of Green (1964, see below) appears to have what I want, but I've never seen the actual function -- all references I have just mention the value for $G_8(0)<\Sigma(8)$.

Can anyone here help me locate this paper (given the reference), or alternately communicate the result to me? The paper is only four pages long, so that's an upper bound on the complexity of the function. Thanks.

M. W. Green. "A lower bound on Rado's Sigma function for binary Turing machines". Switching Circut Theory and Logical Design, Proceedings of the Fifth Annual Symposium (1964), pp. 91-94.

2. Dec 7, 2006

### CRGreathouse

I may have found something in the 35th Annual Midwest Instruction and Computing Symposium papers. There's a piece by Julstrom called "Ackermann's Function in the Numbers of 1s Generated by Green's Machines" that looks promising.