Approximate Safety Properties in Metric Transition Systems

Qian, Junyan; Shi, Fan; Cai, Yong; Pan, Haiyu

doi:10.1109/tr.2021.3139616

Cited by 5 publications

(3 citation statements)

References 44 publications

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“…To the best of our knowledge, previous definitions of (approximate) safety and liveness in nonboolean domains make implicit assumptions about the spec-ification language [48,34,24,45]. We identify two notable exceptions.…”

Section: Overviewmentioning

confidence: 95%

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: 95%

Quantitative Safety and Liveness

Henzinger¹,

Mazzocchi²,

Ege³

2023

Preprint

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“…Designing effective algorithms capable of reasoning about quantitative aspects of correctness of systems' behavior, as well as identifying and studying quantitative properties that generalize the meaning of their boolean counterparts has been, and is an active research field [24,27,19,17,5,6,2,32]. The notion of weighted safety was for the first time introduced in [32].…”

Section: Introductionmentioning

confidence: 99%

Untitled

2023

SACS

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We define the notion of k-safe infinitary series over idempotent ordered totally generalized product ω-valuation monoids that satisfy specific properties. For each element k of the underlying structure (different from the neutral elements of the additive, and the multiplicative operation) we determine two syntactic fragments of the weighted LTL with the property that the semantics of the formulas in these fragments are k-safe infinitary series. For specific idempotent ordered totally generalized product ω-valuation monoids we provide algorithms that given a weighted Büchi automaton and a weighted LTL formula in these fragments, decide whether the behavior of the automaton coincides with the semantics of the formula.

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“…Designing effective algorithms capable of reasoning about quantitative aspects of correctness of systems' behavior, as well as identifying and studying quantitative properties that generalize the meaning of their boolean counterparts has been, and is an active research field [27], [7], [14], [19], [6], [3], [5], [18]. The notion of safety for series over finite words was for the first time introduced in [18].…”

Section: Introductionmentioning

confidence: 99%

A Translation of Weighted LTL Formulas to Weighted Buchi Automata over omega-valuation Monoids

Mandrali¹

2021

SACS

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In this paper we introduce a weighted LTL over product omega-valuation monoids that satisfy specific properties. We also introduce weighted generalized Buchi automata with epsilon-transitions, as well as weighted Buchi automata with epsilon-transitions over product omega-valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted Buchi automata already introduced in the literature. We prove that every formula of a syntactic fragment of our logic can be effectively translated to a weighted generalized Buchi automaton with epsilon-transitions. For generalized product omega-valuation monoids that satisfy specific properties we define a weighted LTL, weighted generalized Buchi automata with epsilon-transitions, and weighted Buchi automata with epsilon-transitions, and we prove the aforementioned results for generalized product omega-valuation monoids as well. The translation of weighted LTL formulas to weighted generalized Buchi automata with epsilon-transitions is now obtained for a restricted syntactical fragment of the logic.

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Approximate Safety Properties in Metric Transition Systems

Cited by 5 publications

References 44 publications

Quantitative Safety and Liveness

Quantitative Safety and Liveness

Untitled

A Translation of Weighted LTL Formulas to Weighted Buchi Automata over omega-valuation Monoids

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