Elements of Finite Model Theory

Libkin, Leonid

doi:10.1007/978-3-662-07003-1

Cited by 734 publications

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“…For example, given the layout of the station with tracks represented as edges between signalling equipment nodes, graph reachability queries are required to verify some of the rules. This corresponds to computing the transitive closure of the graph adjacency relation, which is not expressible in first-order logic [28,Chap. 3].…”

Section: Datalogmentioning

confidence: 99%

Efficient verification of railway infrastructure designs against standard regulations

Luteberget

Johansen

2017

Form Methods Syst Des

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In designing safety-critical infrastructures s.a. railway systems, engineers often have to deal with complex and large-scale designs. Formal methods can play an important role in helping automate various tasks. For railway designs formal methods have mainly been used to verify the safety of so-called interlockings through model checking, which deals with state change and rather complex properties, usually incurring considerable computational burden (e.g., the state-space explosion problem). In contrast, we focus on static infrastructure models, and are interested in checking requirements coming from design guidelines and regulations, as usually given by railway authorities or safety certification bodies. Our goal is to automate the tedious manual work that railway engineers do when ensuring compliance with regulations, through using software that is fast enough to do verification on-the-fly, thus being able to be included in the railway design tools, much like a compiler in an IDE. In consequence, this paper describes the integration into the railway design process of formal methods for automatically extracting railway models from the CAD railway designs and for describing relevant technical regulations and expert knowledge as properties to be checked on the models. We employ a variant of Datalog and use the standardized "railway markup language" railML as basis and exchange format for the formalization. We developed a prototype tool and integrated it in industrial railway CAD software, developed under the name RailCOMPLETE . This on-the-fly verification tool is a help for the engineer while doing the designs, and is not a replacement to other more heavy-weight software like for doing interlocking verification or capacity analysis. Our tool, through the export into railML, can be easily integrated with these other tools. We apply our tool chain in a Norwegian railway project, the upgrade of the Arna railway station.

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Section: Datalogmentioning

confidence: 99%

Efficient verification of railway infrastructure designs against standard regulations

Luteberget

Johansen

2017

Form Methods Syst Des

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“…Let C ∞ω (see [3,50]) be the logic whose formulas are obtained from atomic formulas by using negation, infinitary conjunction and disjunction, and counting quantifiers (∃ i x for any i ≥ 0). The fragment C k ∞ω consists of those formulas of C ∞ω in which at most k distinct variables appear, and C ω ∞ω = k∈ω C k ∞ω .…”

Section: Datalog and Infinitary Logicsmentioning

confidence: 99%

“…Recall that complexity class non-uniform AC 0 consists of all languages accepted by polynomial-size constant-depth families of Boolean circuits (see, e.g., [50]). It is known that any FO-definable class of structures belongs to this complexity class (see Theorem 6.4 of [50]).…”

Section: Theorem 1 ([48]) If a Structure B Does Not Have Finite Dualmentioning

confidence: 99%

“…It is known that any FO-definable class of structures belongs to this complexity class (see Theorem 6.4 of [50]). Moreover, any problem which is LOGSPACE-hard under first-order reductions cannot lie in non-uniform AC 0 because there are problems in LOGSPACE which are not in non-uniform AC 0 (see [24]) and non-uniform AC 0 is closed under first-order reductions.…”

Section: Theorem 1 ([48]) If a Structure B Does Not Have Finite Dualmentioning

confidence: 99%

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Dualities for Constraint Satisfaction Problems

Bulatov

Krokhin

Larose

2008

Lecture Notes in Computer Science

110

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“…We rely on standard definitions and notation from finite model theory (see [6,12]) and the theory of parameterized complexity [9]. We briefly recall some of the definitions we need, but we assume the reader is familiar with this literature.…”

Section: Preliminariesmentioning

confidence: 99%

Parameterized Complexity Classes under Logical Reductions

Dawar

2009

Mathematical Foundations of Computer Science 2009

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Abstract. The parameterized complexity classes of the W -hierarchy are usually defined as the problems reducible to certain natural complete problems by means of fixed-parameter tractable (fpt) reductions. We investigate whether the classes can be characterised by means of weaker, logical reductions. We show that each class W [t] has complete problems under slicewise bounded-variable firstorder reductions. These are a natural weakening of slicewise bounded-variable LFP reductions which, by a result of Flum and Grohe, are known to be equivalent to fpt-reductions. If we relax the restriction on having a bounded number of variables, we obtain reductions that are too strong and, on the other hand, if we consider slicewise quantifier-free first-order reductions, they are considerably weaker. These last two results are established by considering the characterisation of W [t] as the closure of a class of Fagin-definability problems under fpt-reductions. We show that replacing these by slicewise first-order reductions yields a hierarchy that collapses, while allowing only quantifier-free first-order reductions yields a hierarchy that is provably strict.

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Elements of Finite Model Theory

Cited by 734 publications

References 0 publications

Efficient verification of railway infrastructure designs against standard regulations

Efficient verification of railway infrastructure designs against standard regulations

Dualities for Constraint Satisfaction Problems

Parameterized Complexity Classes under Logical Reductions

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