Counterpart Semantics for a Second-Order μ-Calculus

Gadducci, Fabio; Lafuente, Alberto Lluch; Vandin, Andrea

doi:10.1007/978-3-642-15928-2_19

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…The logic was previously introduced for the specification of systems with dynamic topology [8,11], and it is thus now equipped with a powerful abstraction mechanism.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

“…The topological dimension is usually handled by variants of monadic second-order (MSO) logics [6], spatial logics [7] or regular expressions [12], while the temporal dimension is typically tackled with standard modal logics from the model checking tradition like LTL, CTL or the modal µ-calculus. Our own contribution [8] to this field follows the tradition of [2] and it is based on a quantified version of the µ-calculus that mixes temporal modalities and graph expressions in the MSO-style.…”

Section: Introductionmentioning

confidence: 99%

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Exploiting Over- and Under-Approximations for Infinite-State Counterpart Models

Gadducci

Lafuente

Vandin

2012

Lecture Notes in Computer Science

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Abstract. Software systems with dynamic topology are often infinitestate. Paradigmatic examples are those modeled as graph transformation systems (GTSs) with rewrite rules that allow an unbounded creation of items. For such systems, verification can become intractable, thus calling for the development of approximation techniques that may ease the verification at the cost of losing in preciseness and completeness. Both over-and under-approximations have been considered in the literature, respectively offering more and less behaviors than the original system. At the same time, properties of the system may be either preserved or reflected by a given approximation. In this paper we propose a general notion of approximation that captures some of the existing approaches for GTSs. Formulae are specified by a generic quantified modal logic, one that also generalizes many specification logics adopted in the literature for GTSs. We also propose a type system to denote part of the formulae as either reflected or preserved, together with a technique that exploits under-and over-approximations to reason about typed as well as untyped formulae.

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“…The logic was previously introduced for the specification of systems with dynamic topology [8,11], and it is thus now equipped with a powerful abstraction mechanism.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploiting Over- and Under-Approximations for Infinite-State Counterpart Models

Gadducci

Lafuente

Vandin

2012

Lecture Notes in Computer Science

Self Cite

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“…These logics fit at the right level of abstraction for GTSs, allowing to reason on the topological structure of a state, and on the evolution of its components. We refer to § 8 of [11] for a more complete discussion. Unfortunately, the semantical models for such logics are less clearly cut.…”

Section: State-of-the-art In Gts Logicsmentioning

confidence: 99%

“…In [10,11] we introduced a novel semantics for quantified µ-calculi. We defined counterpart models, generalizing GTrSs, where states are algebras and the evolution relation is given by a family of partial morphisms.…”

Section: Current Contributionsmentioning

confidence: 99%

Specification and Verification of Modal Properties for Structured Systems

Vandin

2012

Lecture Notes in Computer Science

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System specification formalisms should come with suitable property specification languages and effective verification tools. We sketch a framework for the verification of quantified temporal properties of systems with dynamically evolving structure. We consider visual specification formalisms like graph transformation systems (GTS) where program states are modelled as graphs, and the program behaviour is specified by graph transformation rules. The state space of a GTS can be represented as a graph transition system (GTrS), i.e. a transition system with states and transitions labelled, respectively, with a graph, and with a partial morphism representing the evolution of state components. Unfortunately, GTrSs are prohibitively large or infinite even for simple systems, making verification intractable and hence calling for appropriate abstraction techniques. State-of-the-art in GTS LogicsAfter the pioneering works on monadic second-order logic (MSO) [7], various graph logics have been proposed and their connection with topological properties of graphs investigated [8]. The need to reason about the evolution of graph topologies has then led to combining temporal and graph logics in propositional temporal logics using graph formulae as state observations (e.g. [4]). However, due to the impossibility to interleave the graphical and temporal dimensions it was not possible to reason on the evolution of single graph components. To overcome this limitation, predicate temporal logics were proposed (e.g. [2,16]), where edge and node quantifiers can be interleaved with temporal operators.More recent approaches [2] propose quantified µ-calculi combining the fixpoint and modal operators with MSO. These logics fit at the right level of abstraction for GTSs, allowing to reason on the topological structure of a state, and on the evolution of its components. We refer to § 8 of [11] for a more complete discussion. Unfortunately, the semantical models for such logics are less clearly cut. Current solutions are not perfectly suited to model systems with dynamic structure, where components might get merged [2,16], or (re)allocated [2]. These problems are often solved by restricting the class of admissible models or by reformulating the state transition relation, hampering the meaning of the logic.

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