Marcel-Paul Schützenberger and complexity

It may happen in your lifetime that you have the luck to meet extraordinary people. MPS is one of them. I attended his lectures when I was a student at the university (Paris 7). This guy is not really famous, he didn't look for fame. We were always less than 10 in the audience. So who is he ?

MPS is a physician, a mathematician, and a computer scientist. Obviously he is excellent in all three domains. His various knowledge gives him a very realistic vision of computer science. Basically, computers were for him a tool to develop mathematics, and have a great future in biology. The last part sounds obvious today, but he said so more than 20 years ago.

But what makes him so attractive during the lectures is that he has stories to tell. As a founder of modern computer science, he met all the other founders all over the world (ok, mainly in USA), invented a very important theorem in language theory, and so he has a lot of nice anecdotes to tell about this pioneer period. I barely remember a couple of them I keep for another blog entry.

For the moment I want to focus on a sentence he said, which is carved in my brain forever:

"There are 2 kinds of program. The short ones and the long ones."

This can be understood different ways. I think the basic idea is that we should keep our distance from computer power and program complexity, and whatever we are trying to develop, after all it's only a computer program, so let's just break it down in sequence of instructions.

For example in the 80's, the hype was on Artificial Intelligence. For a majority of people AI was the most complex applications we can even think about, so much complex that nobody could complete them, btw. Eventually AI died because it didn't fulfill its promises. Some blamed computer performance, although computer power doubles every 18 months it will never catch up with AI complexity which scales up to infinity. Other blamed the poor expressivity of computer languages, too low level. That's better, but no. The real reason that killed AI is the lack of theory. Without theory, no suitable language and no proof of algorithm termination. Then your computer program can be as long as you want, it won't implement correctly the specifications (or you won't be able to prove it). Conclusion is that the program doesn't make it all by itself, it's only a tool and it won't cope with a hole in the theory.

Note that MPS didn't want to under-evaluate complexity in programming. For the developer, the complexity is relative to the constraints s/he has to deal with, about the programming language, tools, software architecture and design, and available resources. But the program is only the implementation of an algorithm, and a correct and efficient algorithm relies on a strong theory.