But the LBA is limited to the size of the input string, while a PC has a fixed but insanely large number of states (2^{number of bits of storage}) and can't in theory accept arbitrarily large strings.
In the somewhat twisted view of the machine I'm putting forward, it's not accessing 'arbitrary memory locations' as memory locations, rather the content of that memory location is part of the input state.
In the somewhat twisted view of the machine I'm putting forward, it's not accessing 'arbitrary memory locations' as memory locations, rather the content of that memory location is part of the input state.