In lecture, we proved that Kolmogorov complexity is uncomputable. In other words, there is no Turing machine that, on inputs, halts with K(s) written on its tape. In this problem, you will work with another uncomputable function called the "generalized busy beaver function." (a) The generalized busy beaver function B(n) is defined as the largest number of steps that an T-state Turing machine can run before eventually halting when e is used as input. Show that if Bin) is computable, then we can decide LE HALT. (b) Conclude that B(n) is uncomputable. In lecture, we proved that Kolmogorov complexity is uncomputable. In other words, there is no Turing machine that, on inputs, halts with K(s) written on its tape. In this problem, you will work with another uncomputable function called the "generalized busy beaver function." (a) The generalized busy beaver function B(n) is defined as the largest number of steps that an T-state Turing machine can run before eventually halting when e is used as input. Show that if Bin) is computable, then we can decide LE HALT. (b) Conclude that B(n) is uncomputable