Using Parametric Automata for the Verification of the Stop-and-Wait Class of Protocols

The Stop-and-Wait protocol (SWP) has two (unbounded) parameters: the maximum sequence number (MaxSeqNo) and the maximum number of retransmissions (MaxRetrans). Our aim is to verify this protocol for all possible values of these parameters. Model checking such a system requires considering an infinite family of state spaces (reachability graphs). We firstly show that the size of these state spaces is linear in MaxSeqNo and quartic in MaxRetrans. This leads us to develop a symbolic representation for the reachability graphs which can be viewed as a symbolic Finite State Automaton (FSA). We apply automata reduction techniques directly to the symbolic FSA to obtain a language equivalent FSA representing the sequences of externally visible events. This FSA is independent of the parameters. We confirm that this is language equivalent to the Stop-and-Wait service of alternating send and receive events. The results are significant as we have: 1. a novel algebraic representation of the infinite set of reachability graphs and their related FSAs of our SWP model; and 2. verified conformance of the SWP to its service, for all values of the unbounded MaxSeqNo parameter.