Departmental Papers (ESE)

Document Type

Journal Article

Date of this Version

June 2004


Postprint version. Published in Theoretical Computer Science, Volume 318, Issue 3, June 8, 2004, pages 297-322.
Publisher URL:


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



Date Posted: 14 April 2006

This document has been peer reviewed.