Optimal Run Problem for Weighted Register Automata

  • Hiroyuki SekiEmail author
  • Reo Yoshimura
  • Yoshiaki Takata
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11884)


Register automata (RA) are a computational model that can handle data values by adding registers to finite automata. Recently, weighted register automata (WRA) were proposed by extending RA so that weights can be specified for transitions. In this paper, we first investigate decidability and complexity of decision problems on the weights of runs in WRA. We then propose an algorithm for the optimum run problem related to the above decision problems. For this purpose, we use a register type as an abstraction of the contents of registers, which is determined by binary relations (such as \(=\), <, etc.) handled by WRA. Also, we introduce a subclass where both the applicability of transition rules and the weights of transitions are determined only by a register type. We present a method of transforming a given WRA satisfying the assumption to a weighted directed graph such that the optimal run of WRA and the minimum weight path of the graph correspond to each other. Lastly, we discuss the optimal run problem for weighted timed automata as an example.



The authors thank the reviewers for providing valuable comments to the paper. This work was supported by JSPS KAKENHI Grant Number JP19H04083.


  1. 1.
    Almagor, S., Cadilhac, M., Mazowiecki, F., Pérez, G.A.: Weak cost register automata are still powerful. In: Hoshi, M., Seki, S. (eds.) DLT 2018. LNCS, vol. 11088, pp. 83–95. Springer, Cham (2018). Scholar
  2. 2.
    Alur, R., D’Antoni, L., Deshmukh, J.V., Raghothaman, M., Yuan, Y.: Regular functions and cost register automata. In: 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013, New Orleans, 25–28 June 2013, pp. 13–22 (2013).
  3. 3.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994). Scholar
  4. 4.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001). Scholar
  5. 5.
    Babari, P., Droste, M., Perevoshchikov, V.: Weighted register automata and weighted logic on data words. In: Sampaio, A., Wang, F. (eds.) ICTAC 2016. LNCS, vol. 9965, pp. 370–384. Springer, Cham (2016). Scholar
  6. 6.
    Babari, P., Droste, M., Perevoshchikov, V.: Weighted register automata and weighted logic on data words. Theor. Comput. Sci. 744, 3–21 (2018). Scholar
  7. 7.
    Behrmann, G., Fehnker, A., Hune, T., Larsen, K., Pettersson, P., Romijn, J., Vaandrager, F.: Minimum-cost reachability for priced time automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001). Scholar
  8. 8.
    Bojańczyk, M., Klin, B., Lasota, S.: Automata theory in nominal sets. Logical Methods Comput. Sci. 10(3) (2014).
  9. 9.
    Bouyer, P.: A logical characterization of data languages. Inf. Process. Lett. 84(2), 75–85 (2002). Scholar
  10. 10.
    Cheng, E.Y., Kaminski, M.: Context-free languages over infinite alphabets. Acta Informatica 35(3), 245–267 (1998). Scholar
  11. 11.
    Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3), 16:1–16:30 (2009). Scholar
  12. 12.
    Kaminski, M., Francez, N.: Finite-memory automata. Theoret. Comput. Sci. 134(2), 329–363 (1994). Scholar
  13. 13.
    Libkin, L., Tan, T., Vrgoč, D.: Regular expressions for data words. J. Comput. Syst. Sci. 81(7), 1278–1297 (2015). Scholar
  14. 14.
    Libkin, L., Vrgoč, D.: Regular path queries on graphs with data. In: 15th International Conference on Database Theory (ICDT 2012), pp. 74–85 (2012).
  15. 15.
    Lygeros, J., Tomlin, C., Sastry, S.: Controllers for reachability specifications for hybrid systems. Automatica 35(3), 349–370 (1999). Scholar
  16. 16.
    Milo, T., Suciu, D., Vianu, V.: Typechecking for XML transformers. In: 19th ACM Symposium on Principles of Database Systems (PODS 2000), pp. 11–22 (2000).
  17. 17.
    Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log. 5(3), 403–435 (2004). Scholar
  18. 18.
    Sakamoto, H., Ikeda, D.: Intractability of decision problems for finite-memory automata. Theor. Comput. Sci. 231(2), 297–308 (2000). Scholar
  19. 19.
    Senda, R., Takata, Y., Seki, H.: Complexity results on register context-free grammars and register tree automata. In: Fischer, B., Uustalu, T. (eds.) ICTAC 2018. LNCS, vol. 11187, pp. 415–434. Springer, Cham (2018). Scholar
  20. 20.
    Senda, R., Takata, Y., Seki, H.: Generalized register context-free grammars. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds.) LATA 2019. LNCS, vol. 11417, pp. 259–271. Springer, Cham (2019). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Nagoya UniversityNagoyaJapan
  2. 2.Kochi University of TechnologyKamiJapan

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