Synthesis and Verification of Constraints in the PGM Protocol

Specifications of protocols usually involve several parameters, for example the number of retransmissions or the timeout delays. The properties satisfied by the protocol depend often on the relation between these parameters. Automatic synthesis of such relations becomes a difficult problem when the constraints are too complex, e.g., non-linear expressions between integer and/or real parameters. This paper reports about modeling and constraint synthesis in the Pragmatic General Multicast (PGM) protocol. The property that we aim to satisfy is the full reliability property for data transmission. The complexity of the PGM prevents us from doing automatic synthesis of this constraint. Instead, we propose a methodology to deal with this problem using classical modelchecking tools for timed and finite systems. Our methodology consists of several steps. First, we identify the sources of complexity and, for each source, we propose several abstractions preserving the full reliability property. Then, we build an abstract parameterized model on which we test, after instantiation of parameters, that the basic properties of the protocol (deadlock freedom, liveness) are preserved. By analyzing the scenario which invalidate the full reliability property, we find a nonlinear constraint between the parameters of the protocol. We check the relation found by instantiating the parameters with relevant values and applying model-checking.