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.

中文翻译：

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对称网络中自稳定协议的参数化综合

分布式系统中的自稳定是一种在发生瞬态故障或错误初始化时保证收敛到一组合法状态而无需外部干预的技术。最近，在设计用于自动合成通过构造正确的自稳定算法的技术方面出现了大量努力。然而，这些技术中的大多数都没有参数化，这意味着它们只能为固定和预定数量的过程合成解决方案。在本文中，我们报告了对称网络中自稳定算法的参数化综合方面的突破，包括环、线、网格和圆环。首先，我们开发了保证 (1) 在合法状态下关闭，和 (2) 在合法状态外无死锁的截止点。我们还开发了自稳定系统收敛的充分条件。由于我们的一些截止值随着进程局部状态空间的大小而增长，因此合成过程的可扩展性仍然是一个问题。我们通过引入一种新的基于 SMT 的技术来解决这个问题，该技术用于对称网络中自稳定算法的反例引导综合。我们已经完全实现了我们的技术并成功地合成了环形和线拓扑的最大匹配、三着色和最大独立集问题的解决方案。我们通过引入一种新的基于 SMT 的技术来解决这个问题，该技术用于对称网络中自稳定算法的反例引导综合。我们已经完全实现了我们的技术并成功地合成了环形和线拓扑的最大匹配、三着色和最大独立集问题的解决方案。我们通过引入一种新的基于 SMT 的技术来解决这个问题，该技术用于对称网络中自稳定算法的反例引导综合。我们已经完全实现了我们的技术并成功地合成了环形和线拓扑的最大匹配、三着色和最大独立集问题的解决方案。