Abstract interpretation of reactive systems

Dams, Dennis; Gerth, Rob; Grumberg, Orna

doi:10.1145/244795.244800

Cited by 289 publications

(245 citation statements)

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“…Applying the just-stated approach, we redevelop and extend Dams's results [10,11] within a higher-order Galois-connection framework [9]:…”

Section: Outline Of Resultsmentioning

confidence: 99%

“…For the branching-time modalities P (∀R) and Q (∃R), a |= Pφ iff for all a , aR a implies a |= φ a |= Qφ iff there exists a such that aR a and a |= φ Dams proved soundness: a |= φ and c ρ a imply c |= φ. With impressive work, Dams also proved "best precision" [11]: For all ρ-(and ρ −1 -) simulations, R and R preserve the most PQ-(mu-calculus [20,21]) properties.…”

Section: Dams's Mixed-transition Systemsmentioning

confidence: 98%

“…In his thesis [10] and in subsequent work [11], Dams studied over-and underapproximations of state-transition relations, R ⊆ C × C, for a discretely ordered set, C, of states. Given complete lattice (A, A ) and the Galois connection, (P(C), ⊆) α, γ (A, A ), Dams defined an over-approximating transition relation, R ⊆ A × A, and an under-approximating transition relation, R ⊆ A × A, as follows:…”

Section: Dams's Mixed-transition Systemsmentioning

confidence: 99%

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Closed and Logical Relations for Over- and Under-Approximation of Powersets

Schmidt

2004

Static Analysis

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Abstract. We redevelop and extend Dams's results on over-and underapproximation with higher-order Galois connections: (1) We show how Galois connections are generated from U-GLB-L-LUBclosed binary relations, and we apply them to lower and upper powerset constructions, which are weaker forms of powerdomains appropriate for abstraction studies.(2) We use the powerset types within a family of logical relations, show when the logical relations preserve U-GLB-L-LUB-closure, and show that simulation is a logical relation. We use the logical relations to rebuild Dams's most-precise simulations, revealing the inner structure of overand under-approximation. (3) We extract validation and refutation logics from the logical relations, state their resemblance to Hennessey-Milner logic and description logic, and obtain easy proofs of soundness and best precision.Almost all Galois-connection-based static analyses are over-approximating: For Galois connection, (P(C), ⊆) α o , γ (A, A ), an abstract value a ∈ A proclaims a property of all the outputs of a program. For example, even ∈ Parity (see Figure 2 for the abstract domain Parity) asserts, "∀even" -all the program's outputs are even numbers, that is, the output is a set from {S ∈ P(Nat) | S ⊆ γ(even)}.An under-approximating Galois connection, (P(C), ⊇) α u , γ A op , where A op = (A, A ), is the dual. Here, even ∈ Parity op asserts that all even numbers are included in the program's outputs -a strong assertion. Also, we may reuse γ : A → P(C) as the upper adjoint from A op to P(C) op iff γ preserves joins in (A, A ) -another strong demand.Fortunately, there is an alternative view of under-approximation: a ∈ A op asserts an existential property -there exists an output with property a. For example, even ∈ Parity op asserts "∃even" -there is an even number in the program's outputs, which is a set from {S ∈ P(Nat) | S ∩ γ(even) = ∅}. Now, we can generalize both over-and under-approximation to multiple properties, e.g., ∀{even, odd } ≡ ∀(even ∨ odd ) -all outputs are even-or odd-valued; and ∃{even, odd } ≡ ∃even ∧ ∃odd -the output set includes an even value and an odd value. These examples "lift" A and A op into the powerset lattices, P L (A) and P U (A), respectively, and set the stage for the problem studied in this paper.schmidt@cis.ksu.edu.

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“…Applying the just-stated approach, we redevelop and extend Dams's results [10,11] within a higher-order Galois-connection framework [9]:…”

Section: Outline Of Resultsmentioning

confidence: 99%

Section: Dams's Mixed-transition Systemsmentioning

confidence: 98%

Section: Dams's Mixed-transition Systemsmentioning

confidence: 99%

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Closed and Logical Relations for Over- and Under-Approximation of Powersets

Schmidt

2004

Static Analysis

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“…The concept of safe abstraction is well-developed within the Abstract Interpretation framework [8,9,12]. The requirement that Abstract Interpretation imposes on the relation between the concrete model and its safe abstraction can be formalized as a requirement on the relation between the data and the operations of the concrete system and their abstract counterparts as follows: Each value of the concrete domain Σ is mapped by a description function ρ : Σ → α Σ into a value from the abstract domain α Σ.…”

Section: Timer Abstraction and Fairnessmentioning

confidence: 99%

“…The concept of safe abstraction is well-developed within the Abstract Interpretation framework [8,9,12]. The relation between the concrete model and its safe abstraction is formalized there as a requirement on the relation between the data operations of the concrete system and their abstract counterparts.…”

Section: Introductionmentioning

confidence: 99%

Using Fairness to Make Abstractions Work

Bošnački

Ioustinova

Sidorova

2004

Model Checking Software

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Dragan Bo˘na˘ki C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Software ENgineeringUsing Fairness To Make Abstractions Work Dragan Bosnacki, Natalia Ioustinova, Natalia Sidorova Using Fairness To Make Abstractions Work ABSTRACT Abstractions often introduce infinite traces which have no corresponding traces at the concrete level and can lead to the failure of the verification. Refinement does not always help to eliminate those traces. In this paper, we consider a timer abstraction that introduces a cyclic behaviour on abstract timers and we show how one can exclude cycles by imposing a strong fairness constraint on the abstract model. By employing the fact that the loop on the abstract timer is a self-loop, we render the strong fairness constraint into a weak fairness constraint and embed it into the verification algorithm. We implemented the algorithm in the DTSpin model checker and showed its efficiency on case studies. The same approach can be used for other data abstractions that introduce self-loops. Abstract. Abstractions often introduce infinite traces which have no corresponding traces at the concrete level and can lead to the failure of the verification. Refinement does not always help to eliminate those traces. In this paper, we consider a timer abstraction that introduces a cyclic behaviour on abstract timers and we show how one can exclude cycles by imposing a strong fairness constraint on the abstract model. By employing the fact that the loop on the abstract timer is a self-loop, we render the strong fairness constraint into a weak fairness constraint and embed it into the verification algorithm. We implemented the algorithm in the DT Spin model checker and showed its efficiency on case studies. The same approach can be used for other data abstractions that introduce self-loops. REPORT SEN-E0313 DECEMBER 16, 2003 SEN

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LORETO: a tool for reducing state explosion in verification of LOTOS programs

Barbuti¹,

Francesco²,

Santone³

et al. 1999

Softw: Pract. Exper.

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LOTOS is a formal specification language for concurrent and distributed systems. Basic LOTOS is the version of LOTOS without value-passing. A widely used approach to the verification of temporal properties is model checking. Often, in this approach the formal specification is translated into a labeled transition system on which formulae expressing properties are checked. A problem with this verification technique is state explosion: concurrent systems are often represented by automata with a prohibitive number of states. In this paper we show how, given a set ρ of actions, it is possible to automatically obtain for a Basic LOTOS program a reduced transition system to which only the arcs labeled by actions in ρ belong. The set ρ of actions plays a fundamental role in conjunction with a temporal logic defined by the authors in a previous paper: selective mu-calculus. The reduced system with respect to ρ preserves the truth value of all selective mu-calculus formulae with actions from the set ρ. We act at both syntactic and semantic levels. From a syntactic point of view, we define a set of transformation rules obtaining a smaller program. On the semantic side, we define a non-standard semantics which dynamically reduces the transition system during generation. We present a tool implementing both the syntactic and the semantic reduction. R. BARBUTI ET AL.systems, the properties concern eventuality or necessity constraints on the occurrence of the events of the system. Temporal logic has been defined to express this kind of properties: it extends classical logic with eventuality and necessity operators.The LOTOS language (Language Of Temporal Ordering Specification) [1] is a Formal Description Technique standardized by the International Standards Organizations (ISO). It can be used in the specification of concurrent and distributed systems, since it contains synchronization, communication and parallelism as primitive notions. It is based on an algebraic theory of concurrency, allowing us to express equivalence notions and system properties. Basic LOTOS is the version of LOTOS without value-passing; thus it is used to describe the synchronization aspects of the system. Basic LOTOS is particularly well suited for the specification of protocols, since in these systems data are not the main concern, while message exchange is crucial.Many verification environments exist for LOTOS and LOTOS-like languages [2-8] offering tools both for checking equivalences and for verifying properties. These environments differ from each other in the specification languages and in the temporal logic that can be used to express properties. One of the most popular environments is the Concurrency Workbench of North Carolina (CWB-NC) [4,8], which includes several different specification languages, among which are Basic LOTOS and CCS [9]. The specifications can be checked for different equivalences, and different logics can be used to express properties. Moreover, diagnostic information is provided, to locate faults.In the CWB-NC, as well as in...

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Abstract interpretation of reactive systems

Cited by 289 publications

References 18 publications

Closed and Logical Relations for Over- and Under-Approximation of Powersets

Closed and Logical Relations for Over- and Under-Approximation of Powersets

Using Fairness to Make Abstractions Work

LORETO: a tool for reducing state explosion in verification of LOTOS programs

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