Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties $R \leadsto Q$ on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constant-space processes under no fairness and interleaving semantics, where $R$ and $Q$ are global state predicates. First, we show that verifying $R \leadsto Q$ for parameterized protocols on symmetric uni-rings is undecidable, even for deterministic and constant-space processes, and conjunctive state predicates. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy $R \leadsto Q$ is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we devise a sound and complete polynomial-time algorithm that takes the predicates $R$ and $Q$, and automatically generates a parameterized protocol that satisfies $R \leadsto Q$ for unbounded (but finite) ring sizes. Moreover, we present some decidability results for cases where leadsto is required from multiple distinct $R$ predicates to different $Q$ predicates. To demonstrate the practicality of our synthesis method, we synthesize some parameterized protocols, including agreement and parity protocols

Optimal deterministic self-stabilizing vertex coloring in unidirectional anonymous networks

International audienceA distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the systems recovers from this catastrophic situation without external intervention in finite time. Uni-directional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. In this paper, we investigate the intrinsic complexity of achieving self-stabilization in unidirectional anonymous general networks, and focus on the classical vertex coloring problem. Specifically, we prove a lower bound of n states per process (where n is the network size) and a recovery time of at least n(n-1)/2 actions in total. We also provide a deterministic algorithm with matching upper bounds that performs in arbitrary unidirectional anonymous graphs