Self-stabilization in distributed systems is a technique to guarantee convergence to a set of legitimate states without external intervention when a transient fault or bad initialization occurs. Recently, there has been a surge of efforts in designing techniques for automated synthesis of self-stabilizing algorithms that are correct by construction. Most of these techniques, however, are not parameterized, meaning that they can only synthesize a solution for a fixed and predetermined number of processes. In this paper, we report a breakthrough in parameterized synthesis of self-stabilizing algorithms in symmetric networks, including ring, line, mesh, and torus. First, we develop cutoffs that guarantee (1) closure in legitimate states, and (2) deadlock-freedom outside the legitimate states. We also develop a sufficient condition for convergence in self-stabilizing systems. Since some of our cutoffs grow with the size of the local state space of processes, scalability of the synthesis procedure is still a problem. We address this problem by introducing a novel SMT-based technique for counterexample-guided synthesis of self-stabilizing algorithms in symmetric networks. We have fully implemented our technique and successfully synthesized solutions to maximal matching, three coloring, and maximal independent set problems for ring and line topologies.
2019-12-20
2021-06-04 08:37:24