Parametric Language Analysis of the Class of Stop-and-Wait Protocols

Model checking a parametric system when one or more of its parameters is unbounded requires considering an infinite family of models. The Stop-and-Wait Protocol (SWP) has two (unbounded) parameters: the maximum sequence number and the maximum number of retransmissions. Previously, we presented a novel method for the parametric analysisof the SWP by developing algebraic formulas in the two parameters that symbolically represent the corresponding infinite class of reachability graphs. Properties were then verified directly from these expressions. This paper extends this analysis to the verification of the SWP using language equivalence. From the algebraic expressions developed previously, a parametric Finite State Automaton (FSA) representing all sequences of user-observable events (i.e. the protocol language) is derived. We then perform determinisation and minimisation directly on the parametric FSA. The result is a simple, non-parametric FSA that is isomorphic to the service language of alternating send and receive events. This result is significant as it verifies conformance of the SWP to its service for all values of the two unbounded parameters.