Abstract
We present Mixed-time Signal Temporal Logic (\(\textsc {STL-mx}\)), a specification formalism which extends STL by capturing the discrete/ continuous time duality found in many cyber-physical systems (CPS), as well as mixed-signal electronic designs. In \(\textsc {STL-mx}\), properties of components with continuous dynamics are expressed in STL, while specifications of components with discrete dynamics are written in LTL. To combine the two layers, we evaluate formulas on two traces, discrete- and continuous-time, and introduce two interface operators that map signals, properties and their satisfaction signals across the two time domains. We show that STL-mx has the expressive power of STL supplemented with an implicit T-periodic clock signal. We develop and implement an algorithm for monitoring STL-mx formulas and illustrate the approach using a mixed-signal example.
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Notes
- 1.
This is a simplification of the AMS setting: not all interaction between analog and digital components goes through A/D and D/A conversions.
- 2.
We use the same symbols for Boolean and temporal connectives in both continuous-time and discrete-time formulas. The distinction between the two layers is defined by the context. Note that each valid formula is classified unambiguously as discrete-time or continuous-time.
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Acknowledgments
This research was supported in part by the Austrian Science Fund (FWF) under grants 27 S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award), and by the Productive 4.0 project (ECSEL 737459). The ECSEL Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and Austria, Denmark, Germany, Finland, Czech Republic, Italy, Spain, Portugal, Poland, Ireland, Belgium, France, Netherlands, United Kingdom, Slovakia, Norway.
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Ferrère, T., Maler, O., Ničković, D. (2019). Mixed-Time Signal Temporal Logic. In: André, É., Stoelinga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2019. Lecture Notes in Computer Science(), vol 11750. Springer, Cham. https://doi.org/10.1007/978-3-030-29662-9_4
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