Abstract
Given a consistent timed scenario, we use its stable distance table, which is a canonical representation for the entire class of equivalent scenarios, to optimise a scenario. We present a general algorithm that can be combined with different heuristics in order to achieve different optimisation goals. In the limited setting of scenarios this algorithm is stronger than the DBM reduction technique.
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- 1.
We use “optimisation” as it is used in the field of compiler theory, i.e., “improvement” that does not necessarily lead to a result that is strictly optimal in some sense.
- 2.
The notion of “behaviour” is equivalent to that of Alur’s “timed word”.
- 3.
To keep the presentation compact, we do not allow sharp inequalities [13]. Equality is expressed in terms of \(\le \) and \(\ge \).
- 4.
Some of the definitions in the remainder of this subsection are taken from our earlier work [11], and customized for the case of scenarios.
- 5.
This limited definition suffices for the purposes of this paper. Synthesis of timed automata from more than one scenario is addressed elsewhere [14].
- 6.
A constraint such as \(m \le c_i - c_j < M\) is equivalent to two such simple constraints: \(c_i - c_j < M\) and \(c_j - c_i \le -m\). A constraint of the form \(c_i \sim C\) is represented as \(c_i - c_{zero} \sim C\), where \(c_{zero}\) is a hypothetical clock whose value is always zero.
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Saeedloei, N., Kluźniak, F. (2020). Optimization of Timed Scenarios. In: Carvalho, G., Stolz, V. (eds) Formal Methods: Foundations and Applications. SBMF 2020. Lecture Notes in Computer Science(), vol 12475. Springer, Cham. https://doi.org/10.1007/978-3-030-63882-5_8
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