Abstract
A Simple Temporal Network with Uncertainty (STNU) is a structure for representing and reasoning about temporal constraints and uncontrollable-but-bounded temporal intervals called contingent links. An STNU is dynamically controllable (DC) if there exists a strategy for executing its time-points that guarantees that all of the constraints will be satisfied no matter how the durations of the contingent links turn out. The fastest algorithm for checking the dynamic controllability of STNUs is based on an analysis of the graphical structure of STNUs. This paper (1) presents a new method for analyzing the graphical structure of STNUs, (2) determines an upper bound on the complexity of certain structures—the indivisible semi-reducible negative loops; (3) presents an algorithm for generating loops—the magic loops—whose complexity attains this upper bound; and (4) shows how the upper bound can be exploited to speed up the process of DC-checking for certain networks.
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Notes
- 1.
Agents are not part of the semantics of STNUs; they are used here for illustration.
- 2.
Morris and Muscettola [7] showed that an STNU is DC iff a certain matrix is consistent. Morris [5] highlighted semi-reducible paths and showed that an STNU is DC iff its graph has no semi-reducible negative loops. Hunsberger [3] showed that the matrix computed by Morris and Muscettola is the SR-distance matrix, \(\mathcal {D}^*\).
- 3.
For Morris [5], case (2) is not needed because he eliminated the case, \(v=0\), from the applicability conditions for the Lower-Case and Cross-Case rules.
- 4.
Unlike Morris [5], for whom every ESP has negative length, this paper must carefully distinguish pesky prefixes from ESPs of length zero.
- 5.
Proofs for this lemma and all subsequent results are in a companion paper [4].
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Hunsberger, L. (2014). Magic Loops and the Dynamic Controllability of Simple Temporal Networks with Uncertainty. In: Filipe, J., Fred, A. (eds) Agents and Artificial Intelligence. ICAART 2013. Communications in Computer and Information Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44440-5_20
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