 
Summary: Optimal Paths in Weighted Timed Automata ?
Rajeev Alur 1;2 , Salvatore La Torre 1;3 , and George J. Pappas 1
1 University of Pennsylvania
2 Bell Labs
3 Universit`a degli Studi di Salerno
email: falur,pappasgg@cis.upenn.edu, latorre@seas.upenn.edu
Abstract. We consider an optimalreachability problem for a timed au
tomaton 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 a (parametric) shortestpath problem in a finite directed
graph. The directed graph we construct is a refinement of the region au
tomaton due to Alur and Dill. We present an exponential time algorithm
to solve the shortestpath problem for weighted timed automata starting
from a single state, and a doublyexponential time algorithm to solve
this problem starting from a zone of the state space.
1 Introduction
Timed automata [AD94] are widely accepted as formal models of realtime sys
tems: a discrete transition graph is equipped with a finite set of clock variables
so expressing timing constraints becomes possible. Automated analysis of timed
automata relies on the construction of a finite quotient of the infinite space
