Forcing Monotonicity in Parameterized Verification: From Multisets to Words

Abdulla, Parosh Aziz

doi:10.1007/978-3-642-11266-9_1

Cited by 6 publications

(12 citation statements)

References 12 publications

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“…the full MSO logic over data words. Note that this contributes to the area of parametrized verification [1], as model checking can prove that a property holds for any number of processes.…”

Section: Resultsmentioning

confidence: 99%

“…If the guard is satisfied, the automaton outputs one or several actions that may use the data values represented by R ∪ P A . They may also use fresh data values, and we will use the parameters Q = {q 1 …”

Section: Data Words and Data Multi-pushdown Automatamentioning

confidence: 99%

“…Moreover, ρ is -phase iff pw ρ is -phase iff apw ρ is -phase. Figure 5 illustrates an abstract parse word and a concrete parse word of the run lep 1 The data word σ(u) generated by a concrete transition σ(δ) is precisely the Σ-projection of string(σ(δ)). Hence, the data word generated by a run ρ is Proj Σ (pw ρ ).…”

Section: Theorem 8 (La Torre Et Al [15])mentioning

confidence: 99%

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Model Checking Languages of Data Words

Bollig

Aiswarya

Gastin

et al. 2012

Foundations of Software Science and Computational Structures

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Abstract. We consider the model-checking problem for data multipushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent programs with dynamic process creation. To specify properties of data words, we use monadic second-order (MSO) logic, which comes with a predicate to test two word positions for data equality. While satisfiability for MSO logic is undecidable (even for weaker fragments such as first-order logic), our main result states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.

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“…the full MSO logic over data words. Note that this contributes to the area of parametrized verification [1], as model checking can prove that a property holds for any number of processes.…”

Section: Resultsmentioning

confidence: 99%

Section: Data Words and Data Multi-pushdown Automatamentioning

confidence: 99%

Section: Theorem 8 (La Torre Et Al [15])mentioning

confidence: 99%

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Model Checking Languages of Data Words

Bollig

Aiswarya

Gastin

et al. 2012

Foundations of Software Science and Computational Structures

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“…Monotonic abstraction is a well-known technique introduced by P. A. Abdulla and collaborators in a series of papers (like for instance [1,3,8,9]); the technique was originally applied in the context of verification of distributed systems, but successively extended also elsewhere (see e.g. [6,7]).…”

Section: Introductionmentioning

confidence: 99%

Monotonic Abstraction Techniques: from Parametric to Software Model Checking

Alberti

Ghilardi

Sharygina

2014

Electron. Proc. Theor. Comput. Sci.

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Monotonic abstraction is a technique introduced in model checking parameterized distributed systems in order to cope with transitions containing global conditions within guards. The technique has been re-interpreted in a declarative setting in previous papers of ours and applied to the verification of fault tolerant systems under the so-called 'stopping failures' model. The declarative reinterpretation consists in logical techniques (quantifier relativizations and, especially, quantifier instantiations) making sense in a broader context. In fact, we recently showed that such techniques can over-approximate array accelerations, so that they can be employed as a meaningful (and practically effective) component of CEGAR loops in software model checking too. 1 c 1 to c 2 . More precisely, the abstraction kills (deletes) all the processes inside the configuration which violate the universal condition. Since the abstract transition relation is an over-approximation of the original one, proving a safety property in the abstract system implies that the property also holds in the original system." Array-Based SystemsArray-based systems were first introduced in [34]: the underlying idea is that of specifying systems of various nature using array theories like those studied in [24,25] and implemented in common SMTsolvers. Array theories are multi-sorted and very flexible; typically one has three sorts: for indexes, elements and arrays. To specify a distributed system, one can use the index sort to model processes and

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“…The main source of inspiration for designing our transformation is the work on monotonic abstraction [3,4,5,1] developed by Abdulla et al, which is more semantic and needs to be adapted each time a new of class of systems is to be verified. On the contrary, our transformation is purely syntactic and may be applied to arbitrary array-based systems, even those not modelling distributed systems, and put to productive work for verification problems where a semantic approachà la Abdulla et al would be much more difficult to adapt.…”

Section: Introductionmentioning

confidence: 99%

Universal Guards, Relativization of Quantifiers, and Failure Models in Model Checking Modulo Theories

Alberti

Ghilardi²,

Pagani³

et al. 2012

SAT

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Model Checking Modulo Theories is a recent approach for the automated verification of safety properties of a class of infinite state systems manipulating arrays, called arraybased systems. The idea is to repeatedly compute pre-images of a set of (unsafe) states by using certain classes of first-order formulae representing sets of states and transitions, and then reduce fix-point checks to Satisfiability Modulo Theories problems. Unfortunately, if the guards contain universally quantified index variables, the backward procedure cannot be fully automated. In this paper, we overcome the problem by describing a syntactic transformation on array-based systems, which can be seen as an instance of the well-known operation of relativization of quantifiers in first-order logic. Interestingly, when specifying and verifying distributed systems, the proposed syntactic transformation can be interpreted as the adoption of the crash-failure model, which is well-known in the literature of fault-tolerant systems. By eliminating universal quantifiers from guards, the transformation significantly extends the scope of applicability of the symbolic backward reachability procedure. To provide empirical evidence of this claim, we discuss our findings in applying the proposed technique to a significant case-study in the verification of some classical algorithms for reliable broadcast.

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Forcing Monotonicity in Parameterized Verification: From Multisets to Words

Cited by 6 publications

References 12 publications

Model Checking Languages of Data Words

Model Checking Languages of Data Words

Monotonic Abstraction Techniques: from Parametric to Software Model Checking

Universal Guards, Relativization of Quantifiers, and Failure Models in Model Checking Modulo Theories

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