On Computing Fixpoints in Well-Structured Regular Model Checking, with Applications to Lossy Channel Systems

Baier, Christel; Bertrand, Nathalie; Schnoebelen, Philippe

doi:10.1007/11916277_24

Cited by 17 publications

(22 citation statements)

References 40 publications

(72 reference statements)

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“…The computability of Mod(EϕUψ) can be shown with the same technique we used, in Section 3.5, for the computability of Pre * (X). Alternatively, one can use backwardchaining algorithms whose termination is guaranteed by Dickson's Lemma (see [9]). …”

Section: Moreover the Set Mod(ϕ) Defmentioning

confidence: 99%

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Lossy Counter Machines Decidability Cheat Sheet

Schnoebelen

2010

Lecture Notes in Computer Science

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Abstract. Lossy counter machines (LCM's) are a variant of Minsky counter machines based on weak (or unreliable) counters in the sense that they can decrease nondeterministically and without notification. This model, introduced by R. Mayr [TCS 297:337-354 (2003)], is not yet very well known, even though it has already proven useful for establishing hardness results. In this paper we survey the basic theory of LCM's and their verification problems, with a focus on the decidability/undecidability divide.

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Section: Moreover the Set Mod(ϕ) Defmentioning

confidence: 99%

“…Many variations are possible, motivated by different situations. We refer to [3,41,9,10,2,4] for results on such games.…”

Section: Theorem 83mentioning

confidence: 99%

Lossy Counter Machines Decidability Cheat Sheet

Schnoebelen

2010

Lecture Notes in Computer Science

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“…In [8] we show how a symbolic representation for sets defined by such fixpoint expressions can be computed effectively (when some guardedness condition holds). …”

Section: Symbolic Representations For Sets Of Configurationsmentioning

confidence: 99%

Symbolic Verification of Communicating Systems with Probabilistic Message Losses: Liveness and Fairness

Baier

Bertrand

Schnoebelen

2006

Lecture Notes in Computer Science

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Abstract. NPLCS's are a new model for nondeterministic channel systems where unreliable communication is modeled by probabilistic message losses. We show that, for ω-regular linear-time properties and finite-memory schedulers, qualitative model-checking is decidable. The techniques extend smoothly to questions where fairness restrictions are imposed on the schedulers. The symbolic procedure underlying our decidability proofs has been implemented and used to study a simple protocol handling two-way transfers in an unreliable setting.

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“…8 The parameterized system induced by P [i] is given by P = Σ, Θ, Δ , where the initial configuration is Θ = ∀iΘ [i], and the transition relation is Δ = ∀iΔ [i]. Thus, as expected, each process starts in an initial state, and in each point in time, all processes simultaneously proceed according to the protocol.…”

Section: An Fmso-based Description Of a Protocolmentioning

confidence: 99%

“…The good news is that many interesting protocols do have a regular description. Also, various acceleration, abstraction, and symmetry-reduction techniques are successfully combined with regular model checking and lead the model-checking algorithm into termination [10,1,28,9,8]. Regular model checking has successfully been applied for the verification of a variety of protocols, including ones involving systems with queues, counters, and dynamic linked data structures [10,1].…”

Section: Introductionmentioning

confidence: 99%

On Verifying Fault Tolerance of Distributed Protocols

Fisman

Kupferman

Lustig

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Distributed systems are composed of processes connected in some network. Distributed systems may suffer from faults: processes may stop, be interrupted, or be maliciously attacked. Fault-tolerant protocols are designed to be resistant to faults. Proving the resistance of protocols to faults is a very challenging problem, as it combines the parameterized setting that distributed systems are based-on, with the need to consider a hostile environment that produces the faults. Considering all the possible fault scenarios for a protocol is very difficult. Thus, reasoning about fault-tolerance protocols utterly needs formal methods.In this paper we describe a framework for verifying the fault tolerance of (synchronous or asynchronous) distributed protocols. In addition to the description of the protocol and the desired behavior, the user provides the fault type (e.g., failstop, Byzantine) and its distribution (e.g., at most half of the processes are faulty). Our framework is based on augmenting the description of the configurations of the system by a mask describing which processes are faulty. We focus on regular model checking and show how it is possible to compile the input for the model-checking problem to one that takes the faults and their distribution into an account, and perform regular model-checking on the compiled input. We demonstrate the effectiveness of our framework and argue for its generality.

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On Computing Fixpoints in Well-Structured Regular Model Checking, with Applications to Lossy Channel Systems

Cited by 17 publications

References 40 publications

Lossy Counter Machines Decidability Cheat Sheet

Lossy Counter Machines Decidability Cheat Sheet

Symbolic Verification of Communicating Systems with Probabilistic Message Losses: Liveness and Fairness

On Verifying Fault Tolerance of Distributed Protocols

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