A Hybrid Method for the Verification and Synthesis of Parameterized Weakly Stabilizing Protocols

We present a hybrid method for verification and synthesis of parameterized self-stabilizing protocols where algorithmic design and mechanical verification techniques/tools are used hand-in-hand. The core idea behind the proposed method includes the automated synthesis of self-stabilizing protocols in a limited scope (i.e., fixed number of processes) and the use of theorem proving methods for the generalization of the solutions produced by the synthesizer. Specifically, we use the Prototype Verification System (PVS) to mechanically verify an algorithm for the synthesis of weakly self-stabilizing protocols. Then, we reuse the proof of correctness of the synthesis algorithm to establish the correctness of the generalized versions of synthesized protocols for an arbitrary number of processes. We demonstrate the proposed approach in the context of an agreement and a coloring protocol on the ring topology.