STL⁎: Extending signal temporal logic with signal-value freezing operator

Brim, Luboš; Dluhoš, Petr; Šafránek, David; Vejpustek, Tomáš

doi:10.1016/j.ic.2014.01.012

Cited by 45 publications

(55 citation statements)

References 14 publications

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“…3. We introduce the expressive logic FLTL (based on the logic STL* ( [8,9]), which augments LTL with value and time freeze variables, and general constraint predicates. We prove a logic transference result with respect to this logic: flows which are close under the Skorokhod metric satisfy "close" FLTL formulae.…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…We prove a logic transference result with respect to this logic: flows which are close under the Skorokhod metric satisfy "close" FLTL formulae. Value and time freeze variables allow expression of complex properties of traces, such as signal tracking ( [8,9]). 4.…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…The logic we consider generalizes MTL, STL, TLTL [4], and STL * [8,9]. We show that if the Skorokhod distance between two traces is small, they satisfy close FLTL formulae.…”

Section: Transference Of Logical Propertiesmentioning

confidence: 97%

“…. , x n ) ≥ 0, as in Signal Temporal Logic (STL) [16] (we however allow f to be non-linear), for specifying constraints on trace values; and (ii) freeze quantifiers, as in TPTL [4] and STL * [8,9] 1 for specifying temporal and value constraints relating different parts of traces (freeze quantifiers can express more complex timing constraints than bounded timing constraints, e.g., of MTL, and can also specify complex value constraints such as signal tracking which cannot be expressed by STL). TLTL subsumes MTL in the boolean setting; and FLTL subsumes STL in the real-valued setting.…”

Section: T∈[0t ] D O X (R(t)) Y(t) mentioning

confidence: 99%

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Quantifying conformance using the Skorokhod metric

Deshmukh¹,

Majumdar

Prabhu

2017

Form Methods Syst Des

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The conformance testing problem for dynamical systems asks, given two dynamical models (e.g., as Simulink diagrams), whether their behaviors are "close" to each other. In the semi-formal approach to conformance testing, the two systems are simulated on a large set of tests, and a metric, defined on pairs of real-valued, real-timed trajectories, is used to determine a lower bound on the distance. We show how the Skorokhod metric on continuous dynamical systems can be used as the foundation for conformance testing of complex dynamical models. The Skorokhod metric allows for both state value mismatches and timing distortions, and is thus well suited for checking conformance between idealized models of dynamical systems and their implementations. We demonstrate the robustness of the metric by proving a transference theorem: trajectories close under the Skorokhod metric satisfy "close" logical properties in the timed linear time logic FLTL (Freeze LTL) containing a rich class of temporal and spatial constraint predicates involving time and value freeze variables. We provide efficient window-based streaming algorithms to compute the Skorokhod metric for both piecewise affine and piecewise constant traces, and use these as a basis for a conformance testing tool for Simulink. We experimentally demonstrate the effectiveness of our tool in finding discrepant behaviors on a set of control system benchmarks, including an industrial challenge problem.

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Section: Summary Of Resultsmentioning

confidence: 99%

Section: Summary Of Resultsmentioning

confidence: 99%

“…The logic we consider generalizes MTL, STL, TLTL [4], and STL * [8,9]. We show that if the Skorokhod distance between two traces is small, they satisfy close FLTL formulae.…”

Section: Transference Of Logical Propertiesmentioning

confidence: 97%

Section: T∈[0t ] D O X (R(t)) Y(t) mentioning

confidence: 99%

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Quantifying conformance using the Skorokhod metric

Deshmukh¹,

Majumdar

Prabhu

2017

Form Methods Syst Des

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“…In this work, we solve the problem in an exact manner using signal-processing computations in the style of [18,33], avoiding reliance on a (costly) quantifier elimination routine. The exhaustive computation of the validity domain is similar to that of [12], who study the problem of monitoring STL*, a variant of STL with freeze quantification [4]. There the parameter space is over subsets of T k for k frozen variables, but could be rephrased over R k , something we intend to explore further.…”

Section: Related Workmentioning

confidence: 99%

Efficient Parametric Identification for STL

Bakhirkin

Ferrère

Maler

2018

Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (Part of CPS Week)

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We describe a new algorithm for the parametric identification problem for signal temporal logic (STL), stated as follows. Given a densetime real-valued signal w and a parameterized temporal logic formula φ, compute the subset of the parameter space that renders the formula satisfied by the signal. Unlike previous solutions, which were based on search in the parameter space or quantifier elimination, our procedure works recursively on φ and computes the evolution over time of the set of valid parameter assignments. This procedure is similar to that of monitoring or computing the robustness of φ relative to w. Our implementation and experiments demonstrate that this approach can work well in practice.

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