"Optimal paths in weighted timed automata" by Rajeev Alur, Salvatore La Torre et al.

Departmental Papers (ESE)

Title

Optimal paths in weighted timed automata

Author(s)

Rajeev Alur, University of Pennsylvania
Salvatore La Torre, Università degli Studi di Salerno
George J. Pappas, University of Pennsylvania

Document Type

Journal Article

Date of this Version

June 2004

Comments

Postprint version. Published in Theoretical Computer Science, Volume 318, Issue 3, June 8, 2004, pages 297-322.
Publisher URL: http://dx.doi.org/10.1016/j.tcs.2003.10.038

Abstract

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)|+|w_max|)), where n is the number of clocks, |δ(A)| is the size of the clock constraints and |w_max| 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.