Abstract
Inspired by the pioneering work of Gilles Kahn on concurrent systems, we model real-time systems as a network of software components each of which is specified to compute a collection of functions according to given timing constraints. The components communicate with each other and their environment via two types of channels: (1) FIFO queues for buffering data, and (2) Registers for sampling time-dependent data streams from sensors or output streams of other components executed at different rates. We present a fixed-point semantics for this model which shows that each system function of a network computes for a given set of input (timed) streams, a unique (timed) output stream. Thanks to the deterministic semantics, a model-based approach is enabled for not only building systems but also updating them after deployment, allowing model-in-the-loop simulation to verify the complete behaviour of the resulting system.
This work is partially supported by the projects: ERC CUSTOMER and KAW UPDATE.
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Notes
- 1.
Addressing the different steps in details, including specification, modelling, verification and compilation is not in the scope of this paper.
- 2.
Note that a stream in \(\mathbb {S}^\varSigma \) is also a stream in \(\mathbb {S}\) (for an appropriate Data domain).
- 3.
where for readability reasons, instead of notation \(\mathbf {app}(a,X)\), we use its definition \(a {\tiny \bullet }X\).
- 4.
such as \(G_Y\) which produces element “1” only if \(c+1\ge th\) otherwise produces nothing, that is, \(\epsilon \).
- 5.
in a corresponding TKPN implementation.
- 6.
Making \(\delta \) an input which may vary over time is straightforward.
- 7.
which must exist.
- 8.
it may use a strongly abstracted version of \(\mathbf{F}\) which only preserves the structure of the output.
- 9.
E.g., if \(\mathbf{F}\) produces one element on each output stream, that is an m-tuple \((d_1 ...d_m)\), then it produces the m-tuple (t...t).
- 10.
\(G_M\) has the same deadline as G, meaning that the data put in the “memory” is immediately available.
- 11.
In the general case, the equations are more complicated as a variable length segment is to be read from P as indicated by the definition of function \(\mathbf {trig}\).
- 12.
which is the trigger time of the node reading the register.
- 13.
which must exist if the stream is infinite. If it is finite, the definition of \(\mathbf {Reg}\) is a bit more complicated, but it is easy to see that this can be fixed.
- 14.
Note some similarity with the definition of function \(\mathbf {trig}\).
- 15.
in fact, due to our simplifying assumptions in Example 4, only oversampling.
- 16.
note that registers are used for reading continuous data streams.
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Yi, W., Mohaqeqi, M., Graf, S. (2022). MIMOS: A Deterministic Model for the Design and Update of Real-Time Systems. In: ter Beek, M.H., Sirjani, M. (eds) Coordination Models and Languages. COORDINATION 2022. IFIP Advances in Information and Communication Technology, vol 13271. Springer, Cham. https://doi.org/10.1007/978-3-031-08143-9_2
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