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On the Dissemination of Open Problems

5 December 2003

Last July, I organized a workshop on Process Algebra: Open Problems and Future Directions with Zoltán Ésik, Wan Fokkink and Anna Ingólfsdóttir. I am very glad to have helped organize that event, and it is my intention to propose more informal meetings of that kind in the splendid location of the University Residential Centre of Bertinoro under the sponsorship of BICI (Bertinoro International Center for Informatics).

One of the aims of that workshop was to give a modest contribution to the development of process algebraic research by identifying open problems in the field of process algebra, and fostering collaboration on their solutions. This was achieved, at least in part, and a preliminary list of research problems is available from the workshop's open problems page. I welcome additions to this page, so feel free to send me a description of your favourite problems for inclusion in that list. This brings me to the main theme of this posting in this web diary:

Should a researcher share his/her research problems with the rest of the community? I happened to wonder about this problem a posteriori, while struggling to solve one of the problems that I had already posted on that page, and mentioned to several colleagues of mine. I knew that others were working on that problem, or were at least aware of it, and I also knew that my coworkers and I had a solution in our hands. For possibly the first time in my career, I felt that we had to hurry to be first to the line, and worked with an intensitity that I had not experienced for a long time. (Well, being what I am, what is "intense" for me is just "a normal day at the office" for most other people.) The result is the paper CCS with Hennessy's Merge has no Finite Equational Axiomatization with Wan Fokkink, Anna Ingólfsdóttir and Bas Luttik.

So, what have I learned from this experience? Well, I have mixed feelings about the disclosure of open problems. On the one hand, an idealist would probably say that the solution of a problem is more important than the person solving it. Therefore, publicizing open problems eventually benefits the whole community and the development of a field of study. A prototypical example of this type of role played by open problems is given by the so-called Erdös Problems that have stimulated, and still stimulate research in several areas of mathematics (most notably in combinatorics).

At the same time, good research problems are hard to find, and people usually reserve them for themselves or their close colleagues. This is the spirit of Oded Godreich's answer to the question:

Could you offer some "good" research problems? On his FAQ page he writes

"No. Of course, there are many well-known open problems (few offered by myself); these can be found in various surveys and papers, but suggesting these to somebody seeking a `"good'' (i.e., tractable and nice) research problem is not very wise. Suggesting `tractable and nice' research problems is very difficult, and in the rare cases that I manage to come across such a problem, I work on it myself or suggest it to my own students."

Overall, I am glad to have contributed some problems to the open problems page resulting from the discussions in Bertinoro, and that several other colleagues have done so too. However, I am also happy to have helped solve one of those problems myself! Even though it seems reasonable to me to disseminate open problems for which one does not have a line of attack oneself -- i.e., those which we do not find 'tractable' at some point in time --, I can now also understand why some of my colleagues prefer not to disclose them.

Addendum posted on 18 December 2003

A well-organized collection of open problems in computational geometry is maintained by Erik D. Demaine, Joseph S. B. Mitchell, and Joseph O'Rourke. I have no doubt that this collection stimulates research in computational geometry and related fields, and helps keep interested researcher up to date with developments in that field.