Ready to Preorder

Ready to Preorder: Get Your BCCSP Axiomatization for Free! is the Amazon.com-sounding title of a recent paper by Wan Fokkink, Anna Ingolfsdottir and yours truly. This paper had a nine-month gestation period. We began working on it when Wan paid a visit to Iceland for a week in late May-early June 2006 to deliver a talk at our second ICE-TCS Theory Day, but the paper was only completed in February 2007.

In the paper we offer an algorithm for turning an axiomatization for a behavioural preorder in the linear time-branching time spectrum that includes the ready simulation preorder into an axiomatization for the kernel of the preorder. The algorithm preserves finiteness, ground-completeness and omega-completeness of the axiomatization that it receives as input. The proof of its correctness relies on an analysis of the so-called cover equations for the semantics in the spectrum we study in the paper.

I thoroughly enjoyed working on that paper. The development of the technical details in that work reminded me yet again of a few valuable lessons that I tend to forget when I feel that I am short of time and that I badly need to produce some research output to keep my conscience at bay.

1. It is easy to make mistakes in proofs unless one is very careful in checking even the seemingly most obvious of claims. (This is what happens to me at least.)
2. Haste is never a good advisor.
   
3. When I feel that a paper is done, I should let it rest for a day, and proof read it once more.
   

I feel that I need this self-advice more than ever :-) Reading Terence Tao's General Advice on Submissions is a reminder of what I should be doing. I hope that I do not fall way too short of the Platonic ideals Tao sets forth.

Thanks again to Anna and Wan, the coauthors with whom I have written the largest number of papers, for another very instructive and pleasant collaborations. I hope that there will be another one in the near future.