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We consider the optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to computing (parametric) shortest paths in a finite weighted directed graph. We call this graph a parametric sub-region graph. It refines the region graph, a standard tool for the analysis of timed automata, by adding the information which is relevant to solving the optimal-reachability problem. We present an algorithm to solve the optimal-reachability problem for weighted timed automata that takes time exponential in O(n (|δ(A)|+|wmax|)), where n is the number of clocks, |δ(A)| is the size of the clock constraints and |wmax| is the size of the largest weight. We show that this algorithm can be improved, if we restrict to weighted timed automata with a single clock. In case we consider a single starting state for the optimal-reachability problem, our approach yields an algorithm that takes exponential time only in the length of clock constraints.
Hybrid systems, Model checking, Optimal reachability, Timed automata
Alur, Rajeev; La Torre, Salvatore; and Pappas, George J., "Optimal paths in weighted timed automata" (2004). Departmental Papers (ESE). Paper 174.
Date Posted: 14 April 2006
This document has been peer reviewed.