"Views on work in theoretical computer science" by Wolfgang Thomas

 
In the fifth installment of the series in which Fellows of the EATCS provide their advice to the budding TCS researcher, I am posting the contribution by Wolfgang Thomas. Happy reading!

As one of the EATCS fellows I have been asked to contribute some personal words of advice for younger people and on my research interests. Well, I try my best.

Regarding advice to a student and young researcher interested in TCS, I start with two short sentences:

• Read the great masters (even when their h-index is low).
• Don’t try to write ten times as many papers as a great master did.

And then I add some words on what influenced me when I started research - you may judge whether my own experiences that go back to „historical“ times would still help you.

By the way, advice from historical times, where blackboards and no projectors were used, posed in an entertaining but clearly wise way, is Gian-Carlo Rota’s paper „Ten Lessons I Wish I Had Been Taught“ (http://www.ams.org/notices/199701/comm-rota.pdf). This is a view of a mathematician but still worth reading and delightful for EATCS members. People like me (68 years old) are also addressed - in the last lesson „Be Prepared for Old Age“…

Back in the 1970’s when I started I wanted to do something relevant. For me this meant that there should be some deeper problems involved, and that the subject of study is of long-term interest. I was attracted by the works of Büchi and Rabin just because of this: That was demanding, and it treated structures that will be important also in hundred years: the natural numbers with successor, and the tree of all words (over some alphabet) with successor functions that represent the attachment of letters.

The next point is a variation of this. It is a motto I learnt from Büchi, and it is a warning not to join too small communities where the members just cite each other. In 1977, when he had seen my dissertation work, Büchi encouraged me to continue but also said: Beware of becoming member of an MAS, and he explained that this means „mutual admiration society“. I think that his advice was good.

I am also asked to say something about principles for the postdoctoral phase. It takes determination and devotion to enter it. I can say just two things, from my own experience as a young person and from later times. First, as it happens with many postdocs, in my case it was unclear up to the very last moment whether I would get a permanent position. In the end I was lucky. But it was a strain. I already prepared for a gymnasium teacher’s career. And when on a scientific party I spoke to Saharon Shelah (one of the giants of model theory) about my worries, he said „well, there is competition“. How true. So here I just say: Don’t give away your hopes - and good luck. - The other point is an observation from my time as a faculty member, and it means that good luck may be actively supported. When a position is open the people in the respective department do not just want a brilliant researcher and teacher but also a colleague. So it is an important advantage when one can prove that one has more than just one field where one can actively participate, that one can enter new topics (which anyway is necessary in a job which lasts for decades), and that one can cooperate (beyond an MAS). So for the postdoc phase this means to look for a balance between work on your own and work together with others, and if possible in different teams of cooperation.

Finally, a comment on a research topic that excites me at this moment. I find it interesting to extend more chapters of finite automata theory to the infinite. This has been done intensively in two ways already - we know automata with infinite „state space“ (e.g., pushdown automata where „states“ are combined from control states and stack contents), and we know automata over infinite words (infinite sequences of symbols from a finite alphabet). Presently I am interested in words (or trees or other objects) where the alphabet is infinite, for example where a letter is a natural number, and in general where the alphabet is given by an infinite model-theoretic structure. Infinite words over the alphabet N are well known in mathematics since hundred years (they are called points of the Baire space there). In computer science, one is interested in algorithmic results which have not been the focus in classical set theory and mathematics, so much is to be done here.