Generalized Quantitative Analysis of Metric Transition Systems

Fahrenberg, Uli; Legay, Axel

doi:10.1007/978-3-319-03542-0_14

Cited by 6 publications

(5 citation statements)

References 54 publications

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“…We have shown in [7,[29][30][31][32]] that all commonly used trace distances obey recursive characterizations as above. We give a few examples, all of which are recursively separating, and refer to [30,31] for further details:…”

Section: Examplementioning

confidence: 95%

Compositionality for quantitative specifications

Fahrenberg¹,

Křetínský

Legay³

et al. 2017

Soft Comput

Self Cite

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We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.

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Section: Examplementioning

confidence: 95%

Compositionality for quantitative specifications

Fahrenberg¹,

Křetínský

Legay³

et al. 2017

Soft Comput

Self Cite

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“…"quantitative languages") [18] extend their boolean counterparts by moving from the two-valued truth domain to richer domains such as real numbers. Such properties have been extensively studied from a static verification perspective in the past decade, e.g., in the context of model-checking probabilistic properties [38,37], games with quantitative objectives [10,15], specifying quantitative properties [11,1], measuring distances between systems [2,16,22,29], best-effort synthesis and repair [9,20], and quantitative analysis of transition systems [47,14,21,19]. More recently, quantitative properties have been also studied from a runtime verification perspective, e.g., for limit monitoring of statistical indicators of infinite traces [25] and for analyzing resource-precision trade-offs in the design of quantitative monitors [33,30].…”

Section: Overviewmentioning

confidence: 99%

Quantitative Safety and Liveness

Henzinger¹,

Mazzocchi²,

Ege³

2023

Preprint

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Safety and liveness are elementary concepts of computation, and the foundation of many verification paradigms. The safety-liveness classification of boolean properties characterizes whether a given property can be falsified by observing a finite prefix of an infinite computation trace (always for safety, never for liveness). In quantitative specification and verification, properties assign not truth values, but quantitative values to infinite traces (e.g., a cost, or the distance to a boolean property). We introduce quantitative safety and liveness, and we prove that our definitions induce conservative quantitative generalizations of both (1) the safety-progress hierarchy of boolean properties and (2) the safety-liveness decomposition of boolean properties. In particular, we show that every quantitative property can be written as the pointwise minimum of a quantitative safety property and a quantitative liveness property. Consequently, like boolean properties, also quantitative properties can be min-decomposed into safety and liveness parts, or alternatively, maxdecomposed into co-safety and co-liveness parts. Moreover, quantitative properties can be approximated naturally. We prove that every quantitative property that has both safe and co-safe approximations can be monitored arbitrarily precisely by a monitor that uses only a finite number of states.

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“…We proceed to lift the results of the previous sections to a quantitative setting, where the Boolean notions of modal and thorough refinement are replaced by refinement distances. We have shown in [7,[29][30][31][32]] that a good setting for quantitative analysis is given by the one of recursively specified trace distances on an abstract commutative quantale as defined below; we refer to the above-cited papers for a detailed exposition of how this framework covers all common approaches to quantitative analysis. Denote by Σ ∞ = Σ * ∪ Σ ω the set of finite and infinite traces over Σ.…”

Section: Robust Specification Theoriesmentioning

confidence: 99%

“…An advantage of behavioral specification formalisms is that models and specifications are closely related, hence distances between models can easily be extended to distances between specifications. We have developed a distance-based approach for MTS in [5][6][7]30] and shown in [7,[29][30][31][32]] that a good general setting is given by recursively specified trace distances on an abstract quantale. Here we extend this to DMTS.…”

Section: Introductionmentioning

confidence: 99%