There is a program called Processing that is perfect for some of these; in particular, that umbrella. You could import the umbrella, generate a random point, test to see if the point is inside the umbrella, and if it is, use the point to draw a circle of a random radius. You could even control the density of the circles from left to right. Lullaby might have started as something generated as well.
However, I'd confidently say that some of these were almost certainly arranged by hand (The H and the Social Dog being the most obvious to my eye), and I'd be surprised if all of them weren't touched by a human at some point. Even if the umbrella was generated programmatically, it was probably touched by a human at some point to refine. Truly random art tends to look a lot more erratic than the very-well refined logos you're showing us.
Illustrator can be scripted to do some of this stuff, but it's not really built with scripting in mind. Definitely give Processing a look if you're interested in generative art.