Report Number: CS-TR-91-1360
Institution: Stanford University, Department of Computer Science
Title: Sooner is safer than later.
Author: Henzinger, Thomas A.
Date: May 1991
Abstract: It has been repeatedly observed that the standard safety-liveness classification of properties of reactive systems does not fit for real-time properties. This is because the implicit "liveness" of time shifts the spectrum towards the safety side. While, for example, response--that "something good" will happen, eventually--is a classical liveness property, bounded response--that "something good" will happen soon, within a certain amount of time--has many characteristics of safety. We account for this phenomenon formally by defining safety and liveness relative to a given condition, such as the progress of time.
http://i.stanford.edu/pub/cstr/reports/cs/tr/91/1360/CS-TR-91-1360.pdf