Abstract
Weighted automata is a basic tool for specification in quantitative verification, which allows to express quantitative features of analysed systems such as resource consumption. Quantitative specification can be assisted by automata learning as there are classic results on Angluin-style learning of weighted automata. The existing work assumes perfect information about the values returned by the target weighted automaton. In assisted synthesis of a quantitative specification, knowledge of the exact values is a strong assumption and may be infeasible. In our work, we address this issue by introducing a new framework of partially-observable deterministic weighted automata, in which weighted automata return intervals containing the computed values of words instead of the exact values. We study the basic properties of this framework with the particular focus on the challenges of active learning partially-observable deterministic weighted automata.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)
Beimel, A., Bergadano, F., Bshouty, N.H., Kushilevitz, E., Varricchio, S.: Learning functions represented as multiplicity automata. J. ACM 47(3), 506–530 (2000)
Blackburn, P., van Benthem, J.F., Wolter, F. (eds.): Handbook of Modal Logic. Elsevier, Amsterdam (2006)
Blondin, M., Finkel, A., Göller, S., Haase, C., McKenzie, P.: Reachability in two-dimensional vector addition systems with states is PSPACE-complete. In: 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, pp. 32–43. IEEE Computer Society (2015)
Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. ACM Trans. Comput. Log. 11(4), 23:1–23:38 (2010)
Chatterjee, K., Henzinger, T.A., Otop, J.: Nested weighted automata. ACM Trans. Comput. Log. 18(4), 31:1–31:44 (2017)
Clarke, E.M., Henzinger, T.A., Veith, H., Bloem, R. (eds.): Handbook of Model Checking, vol. 10. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-10575-8
Doyen, L., Raskin, J.F.: Games with imperfect information: theory and algorithms. In: Apt, K.R., Grädel, E. (eds.), Lectures in Game Theory for Computer Scientists, pp. 185–212. Cambridge University Press (2011)
Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata. Springer Science & Business Media, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01492-5
Guelev, D.P., Dima, C.: Epistemic ATL with perfect recall, past and strategy contexts. In: Fisher, M., van der Torre, L., Dastani, M., Governatori, G. (eds.) CLIMA 2012. LNCS (LNAI), vol. 7486, pp. 77–93. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32897-8_7
Henzinger, T.A., Otop, J.: From model checking to model measuring. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013. LNCS, vol. 8052, pp. 273–287. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40184-8_20
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Adison-Wesley Publishing Company, Reading, Massachusets, USA (1979)
Hunter, P., Raskin, J.-F.: Quantitative games with interval objectives. In: Raman, V., Suresh, S.P. (eds.), 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 2014, volume 29 of LIPIcs, pp. 365–377. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)
Marusic, I., Worrell, J.: Complexity of equivalence and learning for multiplicity tree automata. J. Mach. Learn. Res. 16, 2465–2500 (2015)
Michaliszyn, J., Otop, J.: Minimization of limit-average automata. In: Zhou, Z.-H. (ed.), Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual Event/Montreal, Canada, 19–27 August 2021, pp. 2819–2825. ijcai.org (2021)
Michaliszyn, J., Otop, J.: Learning infinite-word automata with loop-index queries. Artif. Intell. 307, 103710 (2022)
Millington, I.: AI for Games. CRC Press, Boca Raton (2019)
Papadimitriou, C.H., Tsitsiklis, J.N.: The complexity of Markov decision processes. Math. Oper. Res. 12(3), 441–450 (1987)
Acknowledgements
This work was supported by the National Science Centre (NCN), Poland under grant 2020/39/B/ST6/00521.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Michaliszyn, J., Otop, J. (2023). Deterministic Weighted Automata Under Partial Observability. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_52
Download citation
DOI: https://doi.org/10.1007/978-3-031-43619-2_52
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-43618-5
Online ISBN: 978-3-031-43619-2
eBook Packages: Computer ScienceComputer Science (R0)