Abstract
Weighted timed automata extend timed automata with costs on both locations and transitions. In this framework we study the optimal reachability and the optimal control synthesis problems for the automata with acyclic control graphs. This class of automata is relevant for some practical problems such as some static scheduling problems or air-traffic control problems. We give a nondeterministic polynomial time algorithm to solve the decision version of the considered optimal reachability problem. This algorithm matches the known lower bound on the reachability for acyclic timed automata, and thus the problem is NP-complete. We also solve in doubly exponential time the corresponding control synthesis problem.
The first and the second authors were supported in part by the NSF award CCR99-70925, by the SRC award 99-TJ-688, and by the DARPA ITO Mobies award F33615-00-C-1707. The first and the third authors were supported in part by the MURST in the framework of the project “Metodi Formali per la Sicurezza” (MEFISTO). The first author was also supported by the NSF ITR award.
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R. Alur, C. Courcoubetis, and T.A. Henzinger. Computing accumulated delays in real-time system. In Proc. of the Fifth International Conference on Computer-Aided Verification, CAV’93, LNCS 697, pages 181–193. Springer, 1993.
R. Alur and D.L. Dill. A theory of timed automata. Theoretical Computer Science, 126: 183–235, 1994.
R. Alur, S. La Torre and S. Mukhopadhyay. Subclasses of Timed Automata with NP-complete Reachability Problem. CIS Department, University of Pennsylvania, 2001. URL: “ht tp://vnu. cis.upenn.eduRlatorre/Papers/ata.ps.gz”.
R. Alur, S. La Torre, and G. J. Pappas. Optimal paths in weighted timed automata. In Proc. of the 4th International Workshop on Hybrid Systems: Computation and Control, HSCC’01, LNCS 2034, pages 49–62. Springer, 2001.
E. Asarin and O. Maler. As soon as possible: Time optimal control for timed automata. In Proc. of the 2nd International Workshop on Hybrid Systems: Computation and Control, LNCS 1569, pages 19–30. Springer, 1999.
Y. Abdedaim and O. Maler. Job-shop scheduling using timed automata. In Proc. of the 13th Intern. Conference on Computer Aided Verification, CAV’01, LNCS 2102, pages 478–492, 2001.
E. Asarin, O. Maler, and A. Pnueli. Symbolic controller synthesis for discrete and timed systems. In Proc. of the 2nd International Workshop on Hybrid Systems, LNCS 999, pages 1–20. Springer, 1995.
G. Behrman, T. Hune, A. Fehnker, K. Larsen, P. Pettersson, R. Romijn, and F. Vaandrager. Minimum-cost reachability for priced timed automata. In Proc. of the 4th International Workshop on Hybrid Systems: Computation and Control, HSCC’01, LNCS 2034, pages 147–161. Springer, 2001.
C. Courcoubetis and M. Yannakakis. Minimum and maximum delay problems in real-time systems. In Proc. of the 3rd International Conference on Computer Aided Verification, LNCS 575, pages 399–409. Springer, 1991.
D. D’Souza and P. Madhusudan. Timed control synthesis for external specifications. In Proc. of the 19th Annual Symposium on Theoretical Aspects of Computer Science, STACS’02, LNCS 2285, pages 571–582. Springer, 2002.
M. Faella, S. La Torre, and A. Murano. Automata-theoretic decision of timed games. In Proc. of the 3rd Intern. Workshop on Verification, Model Checking, and Abstract Interpretation, VMCAI’02, LNCS 2294, pages 94–108. Springer, 2002.
M. Faella, S. La Torre, and A. Murano. Dense Real-time Games. In Proc. of the 17th Annual IEEE Symposium on Logic in Computer Science, LICS’02, IEEE Computer Society Press, 2002.
J. Ferrante and C. Rackoff. A decision procedure for the first order theory on real addition with order. SIAM Journal of Computing,4(1):69–76, 1975.
T. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. of the 10th International Conference on Concurrency Theory, CONCUR’99, LNCS 1664, pages 320–335, 1999.
T. Henzinger and P. Kopke. Discrete-time control for rectangular hybrid automata. Theoretical Computer Science, 221 (1–2): 369–392, 1999.
K. G. Larsen, G. Behrman, E. Brinksma, A. Fehnker, T. Hune, P. Petersson, and J. Romijn. As cheap as possible: Efficient cost-optimal reachability for priced timed automata. In Proc. of the 13th International Conference on Computer Aided Verification, CAV’01, LNCS, pages 493–505. Springer, 2001.
O. Maler, A. Pnueli, and J. Sifakis. On the synthesis of discrete controllers for timed systems. In Proc. of the 12th Annual Symposium on Theoretical Aspects of Computer Science, STACS’95, LNCS 900, pages 229–242. Springer, 1995.
P. Niebert, S. Tripakis, and S. Yovine. Minimum-time reachability for timed automata. In Proc. of the 8-th IEEE Mediterranean Conference on Control and Automation, 2000.
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La Torre, S., Mukhopadhyay, S., Murano, A. (2002). Optimal-Reachability and Control for Acyclic Weighted Timed Automata. In: Baeza-Yates, R., Montanari, U., Santoro, N. (eds) Foundations of Information Technology in the Era of Network and Mobile Computing. IFIP — The International Federation for Information Processing, vol 96. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35608-2_40
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