Abstract
Automated reasoning about systems with infinite domains requires an extension of automata, and in particular, finite automata, to infinite alphabets. One such model is Variable Finite Automata (VFA). VFAs are finite automata whose alphabet is interpreted as variables that range over an infinite domain. On top of their simple and intuitive structure, VFAs have many appealing properties. One such property is a deterministic fragment (DVFA), which is closed under the Boolean operations, and whose containment and emptiness problems are decidable. These properties are rare amongst the many different models for automata over infinite alphabets. In this paper, we continue to explore the advantages of DVFAs, and show that they have a canonical form, which proves them to be a particularly robust model that is easy to reason about and use in practice. Building on these results, we construct an efficient learning algorithm for DVFAs, based on the \(\textsc {L}^*\) algorithm for regular languages.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
we omit the transitions labeled a from every state, for clarity of presentation.
- 2.
It may be the case that \(\mathcal {L}\) can be expressed with even fewer than \(k'\) variables, by a non-ordered VFA. Here, we only consider ordered DVFA.
References
Argyros, G., D’Antoni, L.: The learnability of symbolic automata. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 427–445. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_23
Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)
Bollig, B., Habermehl, P., Leucker, M., Monmege, B.: A robust class of data languages and an application to learning. Logical Methods Comput. Sci. 10, 11 (2014)
Bojanczyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: LICS, pp. 7–16. IEEE Computer Society (2006)
Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and XML reasoning. J. ACM 56(3), 1–48 (2009)
Drews, S., D’Antoni, L.: Learning symbolic automata. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 173–189. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_10
Frenkel, H., Grumberg, O., Sheinvald, S.: An automata-theoretic approach to model-checking systems and specifications over infinite data domains. J. Autom. Reasoning, 1–25 (2018). https://doi.org/10.1007/s10817-018-9494-0
Grumberg, O., Kupferman, O., Sheinvald, S.: Variable automata over infinite alphabets. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 561–572. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13089-2_47
Kaminski, M., Francez, N.: Finite-memory automata. Theoret. Comput. Sci. 134(2), 329–363 (1994)
Kaminski, M., Zeitlin, D.: Extending finite-memory automata with non-deterministic reassignment. In: Csuhaj-Varjú, E., Ézik, Z. (eds.) AFL, pp. 195–207 (2008)
Neven, F., Schwentick, T., Vianu, V.: Towards regular languages over infinite alphabets. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 560–572. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44683-4_49
Pasareanu, C.S., Giannakopoulou, D., Bobaru, M.G., Cobleigh, J.M., Barringer, H.: Learning to divide and conquer: applying the L* algorithm to automate assume-guarantee reasoning. Formal Methods Syst. Des. 32, 175–205 (2008)
Shemesh, Y., Francez, N.: Finite-state unification automata and relational languages. Inf. Comput. 114, 192–213 (1994)
Tan, T.: Pebble automata for data languages: separation, decidability, and undecidability. Ph.D. thesis, Technion - Computer Science Department (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Sheinvald, S. (2019). Learning Deterministic Variable Automata over Infinite Alphabets. In: ter Beek, M., McIver, A., Oliveira, J. (eds) Formal Methods – The Next 30 Years. FM 2019. Lecture Notes in Computer Science(), vol 11800. Springer, Cham. https://doi.org/10.1007/978-3-030-30942-8_37
Download citation
DOI: https://doi.org/10.1007/978-3-030-30942-8_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30941-1
Online ISBN: 978-3-030-30942-8
eBook Packages: Computer ScienceComputer Science (R0)