Decidability of Invariant Validation for Paramaterized Systems

Fontaine, Pascal; Gribomont, E. Pascal

doi:10.1007/3-540-36577-x_8

Cited by 9 publications

(11 citation statements)

References 21 publications

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“…As noted in [1,14], in the presence of sorts, signatures different from EPR can also have a finite Herbrand universe. We characterise them below.…”

Section: Preliminariesmentioning

confidence: 93%

“…When this condition is satisfied we call the signature non-cyclic. Variants of this fragment have been investigated in a different context in [1,12,14]. In this paper we take an algorithmic point of view.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we provide a translation into the non-cyclic fragment of many-sorted logic which allows one to avoid unnecessary flattening. Many-sorted logic has been intensively used in the SMT community and its advantage for first-order modelling has been advocated in e.g., [1,12,14]. The noncyclic fragment can be shown to be equivalent to the St 0 fragment in [1].…”

Section: Introductionmentioning

confidence: 99%

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Non-cyclic Sorts for First-Order Satisfiability

Korovin

2013

Frontiers of Combining Systems

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Abstract. In this paper we investigate the finite satisfiability problem for firstorder logic. We show that the finite satisfiability problem can be represented as a sequence of satisfiability problems in a fragment of many-sorted logic, which we call the non-cyclic fragment. The non-cyclic fragment can be seen as a generalisation of the effectively propositional fragment (EPR) in the many-sorted setting. We show that the non-cyclic fragment is decidable by instantiation-based methods and present a linear time algorithm for checking whether a given clause set is in this fragment. One of the distinctive features of our finite satisfiability translation is that it avoids unnecessary flattening of terms, which can be crucial for efficiency. We implemented our finite model finding translation in iProver and evaluated it over the TPTP library. Using our translation it was possible solve a large class of problems which could not be solved by other systems.

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“…As noted in [1,14], in the presence of sorts, signatures different from EPR can also have a finite Herbrand universe. We characterise them below.…”

Section: Preliminariesmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-cyclic Sorts for First-Order Satisfiability

Korovin

2013

Frontiers of Combining Systems

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“…There were studied theoretical questions concerning decidability of the problem [19,24,25], and a number of verification algorithms was proposed [6,7,16,18,23,26,29,30]. Several of these approaches are designed for systems with different architectures or different types of synchronisation [16,26], comparing to our approach.…”

Section: Related Workmentioning

confidence: 99%

“…Another approaches to verification of safety properties employ invisible invariants [6,18,29,30]. These approaches, which are not guaranteed to terminate, are based on automated computing of an inductive assertion.…”

Section: Related Workmentioning

confidence: 99%

Formal verification of systems with an unlimited number of components

et al. 2008

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2 3In many real component-based systems and patterns of component interaction, there can be identified a stable part (like control component, server, instance handler) and a number of uniform components of the same type (users, clients, instances). Such systems, so called Control-User systems, are often modelled using an infinite set of finite models of particular components, parametrised by the number of uniform components in the system. However if the maximal number of components is not known, this results in infinite-state models, which cannot be directly verified with effective (finite-state) techniques, like model checking. In this case, more involved techniques have to be employed.In this paper, we propose a verification technique for checking LTL-like interaction properties on Control-User systems with unlimited number of components using finite-state verification. Our method is based on com-

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Instantiation of Parameterized Data Structures for Model-Based Testing

Bouquet

Couchot

Dadeau

et al. 2006

B 2007: Formal Specification and Development in B

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Model-based testing is bound, by essence, to use the enumerated data structures of the system under test (SUT). On the other hand, formal modeling often involves the use of parameterized data structures in order to be more general (such a model should be sufficient to test many implementation variants) and to abstract irrelevant details. Consequently, the validation engineer is sooner or later required to instantiate these parameters. At the current time, this instantiation activity is a matter of experience and knowledge of the SUT. This work investigates how to rationalize the instantiation of the model parameters.It is obvious that a poor instantiation may badly influence the quality of the resulting tests. However, recent results in instantiation-based theorem proving and their application to software verification show that it is often possible to guess the smallest most general data enumeration. We first provide a formal characterization of what a most general instantiation is, in the framework of functional testing. Then, we propose an approach to automate the instantiation of the model parameters, which leaves the specifier and the validation engineer free to use the desired level of abstraction, during the model design process, without having to satisfy any finiteness requirement.We investigate cases where delaying the instantiation is not a problem. This work is illustrated by a realistic running example. It is presented in the framework of the BZ-Testing-Tools methodology, which uses a B abstract machine for model-based testing and targets many implementation languages.

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Decidability of Invariant Validation for Paramaterized Systems

Cited by 9 publications

References 21 publications

Non-cyclic Sorts for First-Order Satisfiability

Non-cyclic Sorts for First-Order Satisfiability

Formal verification of systems with an unlimited number of components

Instantiation of Parameterized Data Structures for Model-Based Testing

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