Abstract Monitors for Quantitative Specifications

Henzinger, Thomas A.; Mazzocchi, Nicolas; Saraç, N. Ege

doi:10.1007/978-3-031-17196-3_11

Cited by 4 publications

(3 citation statements)

References 49 publications

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“…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%

“…Here, we prove that properties that are both approximately safe and approximately co-safe can be monitored approximately by a finite-state monitor. First, we recall the notion of abstract quantitative monitor from [30].…”

Section: Finite-state Approximate Monitoringmentioning

confidence: 99%

“…Definition 55 (Abstract monitor [30]). An abstract monitor M = (∼, γ) is a pair consisting of a right-monotonic equivalence relation ∼ on Σ * and a function γ : (Σ * / ∼) → R ±∞ .…”

Section: Finite-state Approximate Monitoringmentioning

confidence: 99%

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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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Section: Overviewmentioning

confidence: 99%

Section: Finite-state Approximate Monitoringmentioning

confidence: 99%

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Quantitative Safety and Liveness

Henzinger¹,

Mazzocchi²,

Ege³

2023

Preprint

View full text Add to dashboard Cite

show abstract

Quantitative Safety and Liveness

Henzinger

Mazzocchi

Saraç

2023

Lecture Notes in Computer Science

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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 $$\min $$ min -decomposed into safety and liveness parts, or alternatively, $$\max $$ max -decomposed 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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Approximate Distributed Monitoring Under Partial Synchrony: Balancing Speed & Accuracy

Bonakdarpour,

Momtaz,

Ničković

et al. 2024

Lecture Notes in Computer Science

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In distributed systems with processes that do not share a global clock, partial synchrony is achieved by clock synchronization that guarantees bounded clock skew among all applications. Existing solutions for distributed runtime verification under partial synchrony against temporal logic specifications are exact but suffer from significant computational overhead. In this paper, we propose an approximate distributed monitoring algorithm for Signal Temporal Logic (STL) that mitigates this issue by abstracting away potential interleaving behaviors. This conservative abstraction enables a significant speedup of the distributed monitors, albeit with a tradeoff in accuracy. We address this tradeoff with a methodology that combines our approximate monitor with its exact counterpart, resulting in enhanced efficiency without sacrificing precision. We evaluate our approach with multiple experiments, showcasing its efficacy in both real-world applications and synthetic examples.

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Abstract Monitors for Quantitative Specifications

Cited by 4 publications

References 49 publications

Quantitative Safety and Liveness

Quantitative Safety and Liveness

Quantitative Safety and Liveness

Approximate Distributed Monitoring Under Partial Synchrony: Balancing Speed & Accuracy

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