Automated Synthesis of Distributed Self-Stabilizing Protocols

In this paper, we introduce an SMT-based method that automatically synthesizes a distributed self-stabilizing protocol from a given high-level specification and network topology. Unlike existing approaches, where synthesis algorithms require the explicit description of the set of legitimate states, our technique only needs the temporal behavior of the protocol. We extend our approach to synthesize ideal-stabilizing protocols, where every state is legitimate. We also extend our technique to synthesize monotonic-stabilizing protocols, where during recovery, each process can execute an most once one action. Our proposed methods are fully implemented and we report successful synthesis of well-known protocols such as Dijkstra's token ring, a self-stabilizing version of Raymond's mutual exclusion algorithm, ideal-stabilizing leader election and local mutual exclusion, as well as monotonic-stabilizing maximal independent set and distributed Grundy coloring

A Self-Stabilizing Communication Primitive

Invited paperInternational audienceThe goal of the paper is to provide designers of self-stabilizing protocols with a fair and reliable communication primitive, which allows any proces that writes a value in its own register to make sure that every neihgbour eventually does read that value. We assume a link register communication model under read/write atomicity, where every process can read but cannot write into its neighbours' registers. The primitive runs a self-stabilizing protocol, which implements a "rendezvous" communication mechanism in the link register asynchronous model. This protocol works in arbitrary networks and also solves the problem of how to simulate reliable self-stabilizing message-passing in asynchronous distributed systems

Fair and Reliable Self-Stabilizing Communication

12 pages -- Edition: World Scientific Version 2: soumission ArXivInternational audienceWe assume a link-register communication model under read/write atomicity, where every process can read from but cannot write into its neighbours' registers. The paper presents two self-stabilizing protocols for basic fair and reliable link communication primitives. The rst primitive guarantees that any process writes a new value in its register(s) only after all its neighbours have read the previous value, whatever the initial scheduling of processes' actions. The second primitive implements a weak rendezvous communication mechanism by using an alternating bit protocol: whenever a process consecutively writes n values (possibly the same ones) in a register, each neighbour is guaranteed to read each value from the register at least once. Both protocols are self-stabilizing and run in asynchronous arbitrary networks. The goal of the paper is in handling each primitive by a separate procedure, which can be used as a black box in more involved self-stabilizing protocols

Self-Stabilization in the Distributed Systems of Finite State Machines

The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems

On the Limits and Practice of Automatically Designing Self-Stabilization

A protocol is said to be self-stabilizing when the distributed system executing it is guaranteed to recover from any fault that does not cause permanent damage. Designing such protocols is hard since they must recover from all possible states, therefore we investigate how feasible it is to synthesize them automatically. We show that synthesizing stabilization on a fixed topology is NP-complete in the number of system states. When a solution is found, we further show that verifying its correctness on a general topology (with any number of processes) is undecidable, even for very simple unidirectional rings. Despite these negative results, we develop an algorithm to synthesize a self-stabilizing protocol given its desired topology, legitimate states, and behavior. By analogy to shadow puppetry, where a puppeteer may design a complex puppet to cast a desired shadow, a protocol may need to be designed in a complex way that does not even resemble its specification. Our shadow/puppet synthesis algorithm addresses this concern and, using a complete backtracking search, has automatically designed 4 new self-stabilizing protocols with minimal process space requirements: 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, 3-state token passing on bidirectional chains, and 4-state orientation on daisy chains

Automated Synthesis of Timed and Distributed Fault-Tolerant Systems

This dissertation concentrates on the problem of automated synthesis and repair of fault-tolerant systems. In particular, given the required specification of the system, our goal is to synthesize a fault-tolerant system, or repair an existing one. We study this problem for two classes of timed and distributed systems. In the context of timed systems, we focus on efficient synthesis of fault-tolerant timed models from their fault-intolerant version. Although the complexity of the synthesis problem is known to be polynomial time in the size of the time-abstract bisimulation of the input model, the state of the art lacked synthesis algorithms that can be efficiently implemented. This is in part due to the fact that synthesis is in general a challenging problem and its complexity is significantly magnified in the context of timed systems. We propose an algorithm that takes a timed automaton, a set of fault actions, and a set of safety and bounded-time response properties as input, and utilizes a space-efficient symbolic representation of the timed automaton (called the zone graph) to synthesize a fault-tolerant timed automaton as output. The output automaton satisfies strict phased recovery, where it is guaranteed that the output model behaves similarly to the input model in the absence of faults and in the presence of faults, fault recovery is achieved in two phases, each satisfying certain safety and timing constraints. In the context of distributed systems, we study the problem of synthesizing fault-tolerant systems from their intolerant versions, when the number of processes is unknown. To synthesize a distributed fault-tolerant protocol that works for systems with any number of processes, we use counter abstraction. Using this abstraction, we deal with a finite-state abstract model to do the synthesis. Applying our proposed algorithm, we successfully synthesized a fault-tolerant distributed agreement protocol in the presence of Byzantine fault. Although the synthesis problem is known to be NP-complete in the state space of the input protocol (due to partial observability of processes) in the non-parameterized setting, our parameterized algorithm manages to synthesize a solution for a complex problem such as Byzantine agreement within less than two minutes. A system may reach a bad state due to wrong initialization or fault occurrence. One of the well-known types of distributed fault-tolerant systems are self-stabilizing systems. These are the systems that converge to their legitimate states starting from any state, and if no fault occurs, stay in legitimate states thereafter. We propose an automated sound and complete method to synthesize self-stabilizing systems starting from the desired topology and type of the system. Our proposed method is based on SMT-solving, where the desired specification of the system is formulated as SMT constraints. We used the Alloy solver to implement our method, and successfully synthesized some of the well-known self-stabilizing algorithms. We extend our method to support a type of stabilizing algorithm called ideal-stabilization, and also the case when the set of legitimate states is not explicitly known. Quantitative metrics such as recovery time are crucial in self-stabilizing systems when used in practice (such as in networking applications). One of these metrics is the average recovery time. Our automated method for synthesizing self-stabilizing systems generate some solution that respects the desired system specification, but it does not take into account any quantitative metrics. We study the problem of repairing self-stabilizing systems (where only removal of transitions is allowed) to satisfy quantitative limitations. The metric under study is average recovery time, which characterizes the performance of stabilizing programs. We show that the repair problem is NP-complete in the state space of the given system