On the Hardness of Adding Nonmasking Fault Tolerance

Klinkhamer, Alex P.; Ebnenasir, Ali

doi:10.1109/tdsc.2014.2315191

Cited by 8 publications

(6 citation statements)

References 14 publications

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“…Weak (respectively, strong) fairness policy ensures that any action that is continuously (respectively, infinitely often) enabled, will be executed infinitely often. We have shown [27] that synthesizing self-stabilization under weak fairness or no fairness assumptions is an NP-hard problem, whereas it is polynomially solvable under strong fairness [19] (because a strongly fair scheduler ensures recovery from lovelocks). In this paper, we make no assumption on fairness.…”

Section: Basic Conceptsmentioning

confidence: 99%

Topology-Specific Synthesis of Self-Stabilizing Parameterized Systems with Constant-Space Processes

Ebnenasir

Klinkhamer

2021

IIEEE Trans. Software Eng.

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This paper investigates the problem of synthesizing 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.

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Section: Basic Conceptsmentioning

confidence: 99%

Topology-Specific Synthesis of Self-Stabilizing Parameterized Systems with Constant-Space Processes

Ebnenasir

Klinkhamer

2021

IIEEE Trans. Software Eng.

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“…For example, the design of parameterized self-stabilizing protocols algorithmically is known to be an open problem. Moreover, the problem of adding convergence to finite state automata is NP-hard (in the size of state space) [12,13,14]. Most existing techniques for the design of self-stabilization rely on a 'manual design and after-the-fact verification' methods which are limited to specific heuristics.…”

Section: List Of Tablesmentioning

confidence: 99%

“…Most existing techniques for the design of self-stabilization rely on a 'manual design and after-the-fact verification' methods which are limited to specific heuristics. Automatic finite-state synthesizers do exist [13,15,16,17] but they are efficient only in small scopes given the complexity of adding convergence problem (i.e., small finite number of processes) [15,16]. This dissertation includes two parts.…”

Section: List Of Tablesmentioning

confidence: 99%

“…1 Atan_Deriv(n)(Y):Interval = COND (conts−numerical−Riemann ("Atan_Deriv") Atan_Deriv_inclusion atan_deriv_cont "[|0,1/30|]" "atan_deriv_fun" "13" "2") QED Listing 10.9: Using conts-numerical-Riemann to estimate atan(x) at x=1/230, and x=1/30 1.548698 1.5704237 3 × 10 −2 0.6778s 2 13 1.5541294 1.5649923 1 × 10 −2 3.112s 2 14 1.5571195 1.5620022 5 × 10 −3 7.240s 2 15 1.5583402 1.5607815 2 × 10 −3 15.399s 2 16 1.5589505 1.5601711 1 × 10 −3…”

Section: Atanmentioning

confidence: 99%

“…A state that has a correct color at j is called locally correct at j. Thus the earlier three cases define a state under three conditions expressed in13). We call this state LocallyCorrected(s,j) as it is always uncorrupted at process j.…”

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confidence: 99%

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