The Need for Headers: An Impossibility Result for Communication over Unreliable Channels

It is proved that any protocol that constructs a reliable data link service using an unreliable physical channel service necessarily includes in the packets some header information that enables the protocol to treat different packets differently. The physical channel considered is permitted to lose, but not reorder or duplicate packets. The formal framework used for the proof is the I/O automaton model. 1 I n t r o d u c t i o n Probably the most common use for formal models of concurrent programming is to verify that protocols meet their specifications. A less common, but nonetheless important use for such models is to prove impossibility results, showing that no protocol can possibly solve a particular problem. We believe that it is important to the coherence of our research field that the same formal models be used as the foundation for both kinds of activities. Some of the features of a formal model that axe needed to support impossibility results axe the same as those needed for verification; for instance, both kinds of models must allow separate description of the problem to be solved and the allowable implementations. However, some other features may be different. A useful model for proving impossibility results should include a notion of "fair" or "admissible" execution, which describes exactly when system components are required to continue taking steps; otherwise, it will be impossible to guarantee that the system satisfies any liveness properties. Also, a model for proving impossibility results needs to designate which activities are under the control of the protocol and which are under the control of the environment; otherwise, a protocol might "solve" a problem in a trivial way, simply by preventing some of the inputs from occurring. A more extensive discussion of these features can be found in [12]. We believe that the I /O automaton model [10, 11] can serve as a reasonable basis for both verifying concurrent algorithms and for proving impossibility results. The model has already been used in verifying a wide range of algorithms (see, for example, [10, 3, 4, 5, 7, 14, 16, 17]). In this paper, we use it to prove an impossibility result, namely, that any protocol that implements a reliable data link service by using an unreliable physical channel service necessaxily includes in The authors were supported in part by the National Science Foundation under gra~t CCR-86-11442, by the Office of Naval Research under contract N00014-85-K-0168 and by the Defense Advanced Research Projects Agency under contracts N00014-83-K-0125 and N00014-89-J-1988. The first author was supported in part by the Research Foundation for Information Technology of the University of Sydney.