Modal Transition Systems: A Foundation for Three-Valued Program Analysis

Huth, Michael; Jagadeesan, Radha; Schmidt, David A.

doi:10.1007/3-540-45309-1_11

Cited by 150 publications

(108 citation statements)

References 37 publications

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“…We formalize this idea using modal transition systems. (The concept of modal transition systems has recently been successfully applied in model checking for single processes [7,14,9]. )…”

Section: Assumptions From Abstractionsmentioning

confidence: 99%

Automatic Synthesis of Assumptions for Compositional Model Checking

Finkbeiner

Schewe

Brill

2006

Lecture Notes in Computer Science

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Abstract. We present a new technique for automatically synthesizing the assumptions needed in compositional model checking. The compositional approach reduces the proof that a property is satisfied by the parallel composition of two processes to the simpler argument that the property is guaranteed by one process provided that the other process satisfies an assumption A. Finding A manually is a difficult task that requires detailed insight into how the processes cooperate to satisfy the property. Previous methods to construct A automatically were based on the learning algorithm L * , which represents A as a deterministic automaton and therefore has exponential worst-case complexity. Our new technique instead represents A as an equivalence relation on the states, which allows for a quasi-linear construction. The model checker can therefore apply compositional reasoning without risking an exponential penalty for computing A.

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“…We formalize this idea using modal transition systems. (The concept of modal transition systems has recently been successfully applied in model checking for single processes [7,14,9]. )…”

Section: Assumptions From Abstractionsmentioning

confidence: 99%

Automatic Synthesis of Assumptions for Compositional Model Checking

Finkbeiner

Schewe

Brill

2006

Lecture Notes in Computer Science

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“…Indeed, we might combine ρ PL(τ ) and ρ PU (τ ) into ρ P τ ⊆ P(C) × (P L (A) × P U (A)). This motivates sandwich-and mixed-powerdomains in a theory of over-under-approximation of sets [5,13,16,18,19].…”

Section: Validating ¬φ Requires a Refutation Logicmentioning

confidence: 99%

“…18 For R ⊆ C × C and R ⊆ A × A, simulation is equivalently defined as R is ρ-simulated by R iff R −1 · ρ ⊆ ρ · (R ) −1 Treating R −1 and (R ) −1 as functions, we can define Galois-connection soundness as (R ) −1 is a sound over-approximation for R −1 with respect to γ iff…”

Section: Related Workmentioning

confidence: 99%

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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“…An event-and state-based temporal logic for Petri nets is given in [17]. In [16], a modal temporal logic without a fixed-point operator and interpreted over socalled Kripke modal transition systems (a modal version of doubly labelled transition systems) is defined. In [4,6], a state/event extension of LTL is presented, together with a model-checking framework whose formulae are interpreted over so-called labelled Kripke structures (essentially doubly labelled transition systems).…”

Section: Introductionmentioning

confidence: 99%

An Action/State-Based Model-Checking Approach for the Analysis of Communication Protocols for Service-Oriented Applications

Beek

Gnesi

Mazzanti

2008

Formal Methods for Industrial Critical Systems

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Abstract. In this paper we present an action/state-based logical framework for the analysis and verification of complex systems, which relies on the definition of doubly labelled transition systems. The defined temporal logic, called UCTL, combines the action paradigm-classically used to describe systems using labelled transition systems-with predicates that are true over states-as captured when using Kripke structures as semantic model. An efficient model checker for UCTL has been realized, exploiting an on-the-fly algorithm. We then show how to use UCTL, and its model checker, in the design phase of an asynchronous extension of the communication protocol SOAP, called aSOAP. For this purpose, we describe aSOAP as a set of communicating UML state machines, for which a semantics over doubly labelled transition systems has been provided.

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Modal Transition Systems: A Foundation for Three-Valued Program Analysis

Cited by 150 publications

References 37 publications

Automatic Synthesis of Assumptions for Compositional Model Checking

Automatic Synthesis of Assumptions for Compositional Model Checking

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

An Action/State-Based Model-Checking Approach for the Analysis of Communication Protocols for Service-Oriented Applications

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