Discrete Event Systems in Rewriting Logic 1 Problem: Formal Methods in Simulation

In this note, we report on some work in progress on using rewriting logics for discrete event simulation. The idea is to combine the proofs in the logic with the observations in the simulations to gain a better understanding of the interaction intricacies that seem to occur in complex simulations. In particular, we use communication protocols as our application domain, since they have all the interaction and unpredictability that makes formal speciications diicult. The historical barriers to the use of formal methods in designing and developing communication protocols derive from their diierent attitudes: veriication models have been used for many years for proofs of behavior (a veriication model cannot tell you when the model is wrong), but simulation models are used for observations of behavior (a simulation model cannot tell you when the model is right). These are almost always diierent models, since they must concentrate on diierent aspects of the behavior. For example, the veriication methods almost always abstract out the notion of time (even temporal logic 16] 17] does not deal with time, only with the possible orderings of events induced by time) and probabilities (it is extremely hard to prove probabilistic statements), whereas the simulations can only show behavior, not explore all possibilities (so mathematical certainty is replaced by statistical certainty). Our approach here is to implement a discrete event simulation style within rewriting logic 10], so that the logic can be used directly to prove assertions about the simulation. This is part of an eeort to apply interesting formal methods 12] 4] in the modeling of communication protocols 6] 7] 8].