Treffer: Synthesis of Distributed Algorithms with Parameterized Threshold Guards

Fault-tolerant distributed algorithms are notoriously hard to get right. In this paper we introduce an automated method that helps in that process: the designer provides specifications (the problem to be solved) and a sketch of a distributed algorithm that keeps arithmetic details unspecified. Our tool then automatically fills the missing parts. Fault-tolerant distributed algorithms are typically parameterized, that is, they are designed to work for any number n of processes and any number t of faults, provided some resilience condition holds; e.g., n > 3t. In this paper we automatically synthesize distributed algorithms that work for all parameter values that satisfy the resilience condition. We focus on threshold- guarded distributed algorithms, where actions are taken only if a sufficiently large number of messages is received, e.g., more than t or n/2. Both expressions can be derived by choosing the right values for the coefficients a, b, and c, in the sketch of a threshold a·n+b·t+c. Our method takes as input a sketch of an asynchronous threshold-based fault-tolerant distributed algorithm — where the guards are missing exact coefficients—and then iteratively picks the values for the coefficients. Our approach combines recent progress in parameterized model checking of distributed algo- rithms with counterexample-guided synthesis. Besides theoretical results on termination of the synthesis procedure, we experimentally evaluate our method and show that it can synthesize sev- eral distributed algorithms from the literature, e.g., Byzantine reliable broadcast and Byzantine one-step consensus. In addition, for several new variations of safety and liveness specifications, our tool generates new distributed algorithms.