Generalized Model Checking: Reasoning about Partial State Spaces

Bruns, Glenn; Godefroid, Patrice

doi:10.1007/3-540-44618-4_14

Cited by 105 publications

(117 citation statements)

References 24 publications

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“…Generalized model checking [23] considers judgments GMC(M, s, ϕ) which hold iff there is an implementation of (M, s) that satisfies ϕ. For pointed modal specifications (M, s) and Hennessy-Milner formulae ϕ this is PSPACE-complete in the size of ϕ [23,20].…”

Section: Discussionmentioning

confidence: 99%

Complexity of Decision Problems for Mixed and Modal Specifications

Antonik

Huth

Larsen

et al.

Foundations of Software Science and Computational Structures

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Abstract.We consider decision problems for modal and mixed transition systems used as specifications: the common implementation problem (whether a set of specifications has a common implementation), the consistency problem (whether a single specification has an implementation), and the thorough refinement problem (whether all implementations of one specification are also implementations of another one). Common implementation and thorough refinement are shown to be PSPACE-hard for modal, and so also for mixed, specifications. Consistency is PSPACEhard for mixed, while trivial for modal specifications. We also supply upper bounds suggesting strong links between these problems.

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Section: Discussionmentioning

confidence: 99%

Complexity of Decision Problems for Mixed and Modal Specifications

Antonik

Huth

Larsen

et al.

Foundations of Software Science and Computational Structures

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“…Let C[M] be the set of all concrete refinements of M. Intuitively, C[M] is the semantic meaning of M. An interpretation of L µ based on the semantic meaning of a partial model was introduced in [2] as thorough semantics. It is defined as follows:…”

Section: B Partial Models and Abstractionmentioning

confidence: 99%

“…The first is Kripke Modal Transition Systems (KMTSs) [14] and their equivalent variants, Modal TSs [16], Partial Kripke Structures (PKSs) [2], and 3-valued KSs [3]. It requires that every must transition is also a may transition.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Transition Systems Revisited

Ou¹,

Gurfinkel

Chećhik³

2008

Lecture Notes in Computer Science

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Abstract-A variety of partial modeling formalisms, aimed to capture and reason about abstractions, have been proposed. Some, e.g., Kripke Modal Transition Systems (KMTSs) put strong restrictions on necessary and possible behaviours. Some, e.g., Mixed Transition Systems (MixTSs), relax these restrictions. Yet others, e.g., Generalized Kripke MTSs (GKMTSs), allow hypertransitions.In this paper, we aim to understand trade-offs between these formalisms w.r.t. their applicability to symbolic model-checking. We establish that these formalisms have the same expressive power while differing in succinctness. We also measure the analyzability of these formalisms, measured as the precision of computing compositional semantics of temporal logic formulas. We show that the standard compositional semantics is not preserved between equivalent GKMTSs and MixTSs, and introduce a novel semantics, called reduced, which remains compositional while being both more precise than the standard one and preserved by the semantic equivalence.We also present a symbolic algorithm to compute the reduced semantics for MixTS models built via predicate abstractions and report on our experience using it in practice.

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“…Likewise, [a |= θ] = F, only if all the concrete states in γ(a) do not satisfy θ. Sometimes, neither case holds, or our reasoning is not sufficiently strong to infer that one of the cases hold [BG00], in which case the value of θ in a is unknown, denoted [a |= θ] = ⊥. Since must transitions underapproximate the transitions of the concrete system, they are used in the three-valued semantics for proving existential properties.…”

Section: A Multi-valued Semanticsmentioning

confidence: 99%

Better Under-Approximation of Programs by Hiding Variables

Ball

Kupferman

Lecture Notes in Computer Science

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Abstract. Abstraction frameworks use under-approximating transitions in order to prove existential properties of concrete systems. Under-approximating transitions refer to the concrete states that correspond to a particular abstract state in a universal manner. For example, there is a must transition from abstract state a to abstract state a only if all the concrete states in a have successors in a . The universal nature of under-approximating transitions makes them closed under transitivity. Consequently, reachability queries about the concrete system, which have applications in falsification and testing, can be answered by reasoning about its abstraction. On the negative side, the universal nature of under-approximating transitions makes them dependent on all the variables of the program. The abstraction, on the other hand, often hides some of the variables. Since the universal quantification in must transitions ranges over all variables, this often prevents the abstraction from associating a must transition with statements that refer to hidden variables. We introduce and study partitioned-must transitions. The idea is to partition the program variables to relevant and irrelevant ones, and restrict the universal quantification inside must transitions to the relevant variables. Usual must transitions are a special case of partitioned-must transitions in which all variables are relevant. Partitioned-must transitions exist in many realistic settings in which usual must transitions do not exist. As we show, they retain the advantages of must transitions: they are closed under transitivity, their calculation can be automated, and the three-valued semantics induced by usual must transitions is refined to a multi-valued semantics that takes into an account the set of relevant variables.

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Generalized Model Checking: Reasoning about Partial State Spaces

Cited by 105 publications

References 24 publications

Complexity of Decision Problems for Mixed and Modal Specifications

Complexity of Decision Problems for Mixed and Modal Specifications

Mixed Transition Systems Revisited

Better Under-Approximation of Programs by Hiding Variables

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