Parameterized model checking of fault-tolerant distributed algorithms by abstraction

John, Annu; Konnov, Igor; Schmid, Ulrich; Veith, Helmut; Widder, Josef

doi:10.1109/fmcad.2013.6679411

Cited by 59 publications

(99 citation statements)

References 25 publications

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“…Finally we encode the control flow of Algorithm 1. The rationale of the modeling decisions are that the resulting Promela model (i) captures the assumptions of distributed algorithms adequately, and (ii) allows for efficient verification either using explicit state enumeration (as discussed in this paper) or by abstraction as discussed in [21]. After discussing the modeling of distributed algorithms, we will provide the specifications in Section 3.4.…”

Section: Threshold-guarded Distributed Algorithmsmentioning

confidence: 99%

“…In Section 3, we obtain models of distributed algorithms expressed in slightly extended Promela [20] to capture the notions required to fully express faulttolerant distributed algorithms and their environments, including resilience conditions involving parameters like n and t, fairness conditions, and atomicity assumptions. This formalization allows us to (i) instantiate system instances for different system sizes in order to perform explicit state model checking using Spin as discussed in Section 4, and (ii) build a basis for our parameterized model checking technique based on parametric interval abstraction discussed in [21].…”

Section: Introductionmentioning

confidence: 99%

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Towards Modeling and Model Checking Fault-Tolerant Distributed Algorithms

John

Konnov

Schmid

et al. 2013

Model Checking Software

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Abstract. Fault-tolerant distributed algorithms are central for building reliable, spatially distributed systems. In order to ensure that these algorithms actually make systems more reliable, we must ensure that these algorithms are actually correct. Unfortunately, model checking state-ofthe-art fault-tolerant distributed algorithms (such as Paxos) is currently out of reach except for very small systems. In order to be eventually able to automatically verify such fault-tolerant distributed algorithms also in larger systems, several problems have to be addressed. In this paper, we consider modeling and verification of fault-tolerant algorithms that basically only contain threshold guards to control the flow of the algorithm. As threshold guards are widely used in fault-tolerant distributed algorithms (and also in Paxos) efficient methods to handle them bring us closer to the above mentioned goal. As case study we use the reliable broadcasting algorithm by Srikanth and Toueg that tolerates even Byzantine faults. We show how one can model this basic fault-tolerant distributed algorithm in Promela such that safety and liveness properties can be efficiently verified in Spin. We provide experimental data also for other distributed algorithms.

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Section: Threshold-guarded Distributed Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Towards Modeling and Model Checking Fault-Tolerant Distributed Algorithms

John

Konnov

Schmid

et al. 2013

Model Checking Software

Self Cite

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show abstract

“…Thus this logic is sometimes called prenex indexed temporal logic. Note that if one allows vertex quantifiers inside the scope of temporal path quantifiers then one quickly reaches undecidability even for systems with no communication [41]. For the remainder of this paper specifications only come from i-CTL * \X, i.e., without the next-time operator X.…”

Section: Indexed Temporal Logicmentioning

confidence: 99%

“…For instance, the formula ∀i = j. AG(¬(critical, i) ∨ ¬(critical, j)) says that no two processes are in their critical sections at the same time. We focus on a fragment of this logic where the process quantifiers only appear at the front of a temporal logic formula-allowing the process quantifiers to appear in the scope of path quantifiers results in undecidability even with no communication between processes [41]. (iii) The sets of topologies we consider all have either bounded tree-width, or more generally bounded cliquewidth, and are expressible in one of three ways.…”

Section: System Modelmentioning

confidence: 99%

Parameterized model checking of rendezvous systems

et al. 2017

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Parameterized model checking is the problem of deciding if a given formula holds irrespective of the number of participating processes. A standard approach for solving the parameterized model checking problem is to reduce it to model checking finitely many finite-state systems. This work considers the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new decidability results for others. Second, we consider the cases where model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system is equivalent to a single finite-state system (more precisely a Büchi word automaton), and establish tight bounds on the sizes of such automata.

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“…Otherwise, the abstract counterexample is spurious and the abstraction has to be refined using the information from the examination. This technique is called the "counterexample guided abstraction refinement" (CEGAR) and it is widely used in model checking [1], [4], [9].…”

Section: Cegar Approachmentioning

confidence: 99%

New Search Strategies for the Petri Net CEGAR Approach

Hajdu

Vörös

Bartha

2015

Application and Theory of Petri Nets and Concurrency

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Abstract. Petri nets are a successful formal method for the modeling and verification of asynchronous, concurrent and distributed systems. Reachability analysis can provide important information about the behavior of the model. However, reachability analysis is a computationally hard problem, especially when the state space is infinite. Abstractionbased techniques are often applied to overcome complexity. In this paper we analyze an algorithm, which uses counterexample guided abstraction refinement. This algorithm proved its efficiency on the model checking contest. We examine the algorithm from a theoretical and practical point of view. On the theoretical side, we show that the algorithm cannot decide reachability for relatively simple instances. We propose a new iteration strategy to explore the invariant space, which extends the set of decidable problems. We also give proofs on the theoretical limits of our approach. On the practical side, we examine different search strategies and we present our new, complex strategy with superior performance compared to traditional strategies. Measurements show that our new contributions perform well for traditional benchmark models as well.

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Parameterized model checking of fault-tolerant distributed algorithms by abstraction

Cited by 59 publications

References 25 publications

Towards Modeling and Model Checking Fault-Tolerant Distributed Algorithms

Towards Modeling and Model Checking Fault-Tolerant Distributed Algorithms

Parameterized model checking of rendezvous systems

New Search Strategies for the Petri Net CEGAR Approach

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