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.
CPS Real-Time, CPS Formal Methods, GRASP
Date of this Version
Theoretical Computer Science
NOTICE: This is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science, Vol 318, Issue 3, 8 June 2004, DOI: 10.1016/j.tcs.2003.10.038.
Hybrid systems, Model checking, Optimal reachability, Timed automata
Date Posted: 14 April 2006
This document has been peer reviewed.