This is an extended version of an essay with the same title that I wrote for the workshop Algebraic Process Calculi: The First Twenty Five Years and Beyond, held in Bertinoro, Italy in the first week of August 2005.

In the k-set agreement problem, each process proposes a value and has to decide a value in such a way that a decided value is a proposed value and at most k different values are decided. This problem can easily be solved in synchronous systems or in asynchronous systems prone to t process crashes when t < k. In contrast, it has been shown that k-set agreement cannot be solved in asynchronous sy...

Bacterial cell-to-cell communication (‘quorum sensing’) is mediated by structurally diverse, small diffusible signal molecules which regulate gene expression as a function of cell population density. Many different Gramnegative animal, plant and fish pathogens employ Nacylhomoserine lactones (AHLs) as quorum sensing signal molecules which control diverse physiological processes including biolum...