Abstract
We prove that if a data language and its complement are both recognized by nondeterministic register automata (without guessing), then they are also recognized by deterministic ones.
B. Klin—Supported by the European Research Council (ERC) under the EU Horizon 2020 programme (ERC consolidator grant LIPA, agreement no. 683080).
S. Lasota—Supported by the NCN grant 2019/35/B/ST6/02322.
S. Toruńczyk—Supported by the NCN grant 2017/26/D/ST6/00201.
Chapter PDF
Similar content being viewed by others
Keywords
References
M. Bojańczyk. Slightly infinite sets. A draft of a book available at https://www.mimuw.edu.pl/~bojan/paper/atom-book.
M. Bojanczyk. Data monoids. In Proc. STACS 2011, volume 9 of LIPIcs, pages 105–116. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2011.
M. Bojańczyk, C. David, A. Muscholl, T. Schwentick, and L. Segoufin. Two-variable logic on data words. ACM Trans. Comput. Log., 12(4):27:1–27:26, 2011.
M. Bojańczyk, B. Klin, and S. Lasota. Automata with group actions. In Proc. LICS 2011, pages 355–364, 2011.
M. Bojańczyk, B. Klin, and S. Lasota. Automata theory in nominal sets. Log. Methods Comput. Sci., 10(3), 2014.
M. Bojańczyk and S. Lasota. An extension of data automata that captures XPath. Log. Methods Comput. Sci., 8(1), 2012.
M. Bojańczyk and R. Stefański. Single-use automata and transducers for infinite alphabets. In Proc. ICALP 2020, volume 168 of LIPIcs, pages 113:1–113:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
L. Clemente and C. Barloy. Bidimensional linear recursive sequences and universality of unambiguous register automata. Submited for publication, 2020.
L. Clemente, S. Lasota, and R. Piórkowski. Timed games and deterministic separability. In Proc. ICALP 2020, volume 168 of LIPIcs, pages 121:1–121:16, 2020.
T. Colcombet. Forms of Determinism for Automata. In STACS’12 (29th Symposium on Theoretical Aspects of Computer Science), volume 14, pages 1–23. LIPIcs, 2012.
T. Colcombet, C. Ley, and G. Puppis. Logics with rigidly guarded data tests. Log. Methods Comput. Sci., 11(3), 2015.
T. Colcombet and A. Manuel. Generalized data automata and fixpoint logic. In Proc. FSTTCS 2014, volume 29 of LIPIcs, pages 267–278. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014.
L. D’Antoni and M. Veanes. Minimization of symbolic automata. In Proc. POPL ’14, pages 541–554. ACM, 2014.
S. Demri and R. Lazic. LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log., 10(3):16:1–16:30, 2009.
N. Francez and M. Kaminski. Finite-memory automata. Theor. Comput. Sci., 134(2):329–363, 1994.
N. Francez and M. Kaminski. An algebraic characterization of deterministic regular languages over infinite alphabets. Theor. Comput. Sci., 306(1-3):155–175, 2003.
M. Kaminski and T. Tan. Regular expressions for languages over infinite alphabets. Fundam. Informaticae, 69(3):301–318, 2006.
M. Kaminski and D. Zeitlin. Finite-memory automata with non-deterministic reassignment. Int. J. Found. Comput. Sci., 21(5):741–760, 2010.
S. Lasota. Decidability border for Petri nets with data: WQO dichotomy conjecture. In Proc. PETRI NETS 2016, volume 9698 of Lecture Notes in Computer Science, pages 20–36. Springer, 2016.
L. Libkin, T. Tan, and D. Vrgoc. Regular expressions for data words. J. Comput. Syst. Sci., 81(7):1278–1297, 2015.
T. Milo, D. Suciu, and V. Vianu. Typechecking for XML transformers. J. Comput. Syst. Sci., 66(1):66–97, 2003.
A. Mottet and K. Quaas. The containment problem for unambiguous register automata. In Proc. STACS 2019, volume 126 of LIPIcs, pages 53:1–53:15, 2019.
F. Neven, T. Schwentick, and V. Vianu. Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log., 5(3):403–435, 2004.
A. M. Pitts. Nominal Sets: Names and Symmetry in Computer Science, volume 57 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 2013.
H. Sakamoto and D. Ikeda. Intractability of decision problems for finite-memory automata. Theor. Comput. Sci., 231(2):297–308, 2000.
L. Segoufin. Automata and logics for words and trees over an infinite alphabet. In Proc. CSL 2006, volume 4207 of Lecture Notes in Computer Science, pages 41–57. Springer, 2006.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2021 The Author(s)
About this paper
Cite this paper
Klin, B., Lasota, S., Toruńczyk, S. (2021). Nondeterministic and co-Nondeterministic Implies Deterministic, for Data Languages. In: Kiefer, S., Tasson, C. (eds) Foundations of Software Science and Computation Structures. FOSSACS 2021. Lecture Notes in Computer Science(), vol 12650. Springer, Cham. https://doi.org/10.1007/978-3-030-71995-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-030-71995-1_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-71994-4
Online ISBN: 978-3-030-71995-1
eBook Packages: Computer ScienceComputer Science (R0)