On system rollback and totalized fields: An algebraic approach to system change

In system operations the term rollback is often used to imply that arbitrary changes can be reversed i.e. ‘rolled back’ from an erroneous state to a previously known acceptable state. We show that this assumption is flawed and discuss error-correction schemes based on absolute rather than relative change.Insight may be gained by relating change management to the theory of computation. To this end, we reformulate previously-defined ‘convergent change operators’ of Burgess into the language of groups and rings. We show that, in this form, the problem of rollback from a convergent operation becomes equivalent to that of ‘division by zero’ in computation. Hence, we discuss how recent work by Bergstra and Tucker on zero-totalized fields helps to clear up long-standing confusion about the options for ‘rollback’ in change management.