Guiding and Cost-Optimality in UPPAAL

Gerd Behrmann, Ansgar Fehnker, Thomas Hune, Kim G. Larsen, Paul Pettersson, and Judi Romijn

In this paper we present an algorithm for efficiently computing the minimum cost of reaching a goal state in the model of Uniformly Priced Timed Automata (UPTA). This model can be seen as a submodel of the recently suggested model of linearly priced timed automata, which extends timed automata with prices on both locations and transitions. The presented algorithm is based on a symbolic semantics of UTPA, and an efficient representation and operations based on difference bound matrices. In analogy with Dijkstra’s shortest path algorithm, we show that the search order of the algorithm can be chosen such that the number of symbolic states explored by the algorithm is optimal, to be optimal, in the sense that the number of explored states can not be reduced by any other search order. We also present a number of techniques inspired by branch-and-bound algorithms which can be used for limiting the search space and for quickly finding near-optimal solutions. The algorithm has been implemented in the verification tool UPPAAL. When applied on a number of experiments the presented techniques reduced the explored state-space with up to 90%.

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