 
Summary: Optimal Reachability for Weighted Timed
Games ?
Rajeev Alur Mikhail Bernadsky P. Madhusudan
University of Pennsylvania
Abstract
Weighted timed automata are timed automata annotated with costs on locations
and transitions. The optimal gamereachability problem for these automata is to nd
the bestcost strategy of supplying inputs so as to ensure reachability of a target set
within a specied number of iterations. The only known complexity bound for this
problem is a doublyexponential upper bound. We establish a singlyexponential
upper bound and show that there exist automata with exponentially many states
in a single region with pairwise distinct optimal strategies.
Key words: Timed automata, timed games, optimal costs, weighted games.
1 Introduction
Timed automata [AD94] extend nitestate automata with realvalued clock
variables, and have proved to be useful in modeling realtime systems. The
canonical problem for timed automata is reachability, and can be solved in
polynomialspace using a nitestate quotientthe socalled region graphof
the underlying innite statespace. A natural generalization of reachability
corresponds to optimal reachability that asks how soon a target state (or a set
