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Optimal Reachability for Weighted Timed Rajeev Alur Mikhail Bernadsky P. Madhusudan

Summary: Optimal Reachability for Weighted Timed
Games ?
Rajeev Alur Mikhail Bernadsky P. Madhusudan
University of Pennsylvania
Weighted timed automata are timed automata annotated with costs on locations
and transitions. The optimal game-reachability problem for these automata is to nd
the best-cost strategy of supplying inputs so as to ensure reachability of a target set
within a speci ed number of iterations. The only known complexity bound for this
problem is a doubly-exponential upper bound. We establish a singly-exponential
upper bound and show that there exist automata with exponentially many states
in a single region with pair-wise distinct optimal strategies.
Key words: Timed automata, timed games, optimal costs, weighted games.
1 Introduction
Timed automata [AD94] extend nite-state automata with real-valued clock
variables, and have proved to be useful in modeling real-time systems. The
canonical problem for timed automata is reachability, and can be solved in
polynomial-space using a nite-state quotient|the so-called region graph|of
the underlying in nite state-space. A natural generalization of reachability
corresponds to optimal reachability that asks how soon a target state (or a set


Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania


Collections: Computer Technologies and Information Sciences