This paper investigates the synthesis of parameterized systems that are self-stabilizing by construction. To this end, we present several significant results. First, we show a counterintuitive result that despite the undecidability of verifying self-stabilization for parameterized unidirectional rings, synthesizing self-stabilizing unidirectional rings is decidable! This is surprising because it is known that, in general, the synthesis of distributed systems is harder than their verification. Second, we present a topology-specific synthesis method (derived from our proof of decidability) that generates the state transition system of template processes of parameterized self-stabilizing systems with elementary unidirectional topologies (e.g., rings, chains, trees). We also provide a software tool that implements our synthesis algorithms and generates interesting self-stabilizing parameterized unidirectional rings in less than 50 microseconds on a regular laptop. We validate the proposed synthesis algorithms for decidable cases in the context of several interesting distributed protocols. Third, we show that synthesis of self-stabilizing bidirectional rings remains undecidable.

This article investigates the verification of livelock-freedom and self-stabilization on parameterized rings consisting of symmetric, constant space, deterministic, and self-disabling processes. The results of this article have a significant impact on several fields, including scalable distributed systems, resilient and self- * systems, and verification of parameterized systems. First, we identify necessary and sufficient local conditions for the existence of global livelocks in parameterized unidirectional rings with unbounded (but finite) number of processes under the interleaving semantics. Using a reduction from the periodic domino problem, we show that, in general, verifying livelock-freedom of parameterized unidirectional rings is undecidable (specifically, Π 1 0 -complete) even for constant space, deterministic, and self-disabling processes. This result implies that verifying self-stabilization for parameterized rings of self-disabling processes is also undecidable. We also show that verifying livelock-freedom and self-stabilization remain undecidable under (1) synchronous execution semantics, (2) the FIFO consistency model, and (3) any scheduling policy. We then present a new scope-based method for detecting and constructing livelocks in parameterized rings. The proposed semi-algorithm behind our scope-based verification is based on a novel paradigm for the detection of livelocks that totally circumvents state space exploration. Our experimental results on an implementation of the proposed semi-algorithm are very promising as we have found livelocks in parameterized rings in a few microseconds on a regular laptop. The results of this article have significant implications for scalable distributed systems with cyclic topologies.

This paper presents a novel two-step method for automated design of self-stabilization. The first step enables the specification of legitimate states and an intuitive (but imprecise) specification of the desired functional behaviors in the set of legitimate states (hence the term “shadow”). After creating the shadow specifications, we systematically introduce the main variables and the topology of the desired self-stabilizing system. Subsequently, we devise a parallel and complete backtracking search towards finding a self-stabilizing solution that implements a precise version of the shadow behaviors, and guarantees recovery to legitimate states from any state. To the best of our knowledge, the shadow/puppet synthesis is the first sound and complete method that exploits parallelism and randomization along with the expansion of the state space towards generating self-stabilizing systems that cannot be synthesized with existing methods. We have validated the proposed method by creating both a sequential and a parallel implementation in the context of a software tool, called Protocon. Moreover, we have used Protocon to automatically design three new self-stabilizing protocols that we conjecture to require the minimal number of states per process to achieve stabilization (when processes are deterministic): 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, and 3-state token passing on bidirectional chains.

This paper investigates the complexity of adding nonmasking fault tolerance, where a nonmasking fault-tolerant program guarantees recovery from states reached due to the occurrence of faults to states from where its specifications are satisfied. We first demonstrate that adding nonmasking fault tolerance to low atomicity programs-where processes have read/write restrictions with respect to the variables of other processes--is NP-complete (in the size of the state space) on an unfair or weakly fair scheduler. Then, we establish a surprising result that even under strong fairness, addition of nonmasking fault tolerance remains NP-hard! The NP-hardness of adding nonmasking fault tolerance is based on a polynomial-time reduction from the 3-SAT problem to the problem of designing self-stabilizing programs from their non-stabilizing versions, which is a special case of adding nonmasking fault tolerance. While it is known that designing self-stabilization under the assumption of strong fairness is polynomial, we demonstrate that adding self-stabilization to non-stabilizing programs is NP-hard under weak fairness.