Homotopy and Concurrency.
Jeremy Gunawardena · 1994
In this paper we give a homotopy theoretic proof of a well-known result in database engineering: that 2-phase locking is safe. The proof gives an immediate intuitive reason for why the 2-phase locking condition implies safety. We point out a number of interesting open questions regarding the interplay between homotopy and concurrency. Keywords: Homotopy theory, serializability, 2-phase locking, concurrency theory 1 Introduction What has homotopy got to do with concurrency? At first sight it seems unlikely that there should be any relationship between these two subjects. After all, homotopy theory is about continuous objects while concurrency typically deals with discrete structures. In this paper I will try to show that, on the contrary, there may be a very natural relationship between the two. Instead of making a lot of abstract statements about homotopy and concurrency I would like to work through the proof of a theorem which all database engineers learn at their Mother's knee: th...