Skip to main content
SpringerLink
Log in

Synchronizing Words for Real-Time Deterministic Pushdown Automata

Extended Abstract

  • Conference paper
  • First Online:
Proceedings of the Seventh International Conference on Mathematics and Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1412))

Abstract

Synchronizing finite(-state) automata have been widely studied in numerous fields of mathematics and computer science for theoretical and practical purposes. This exposition attempts to extend the scope of the synchronization property from one-way deterministic finite automata to one-way real-time deterministic pushdown automata. In particular, it argues on the characteristics of synchronizing words (or reset words), each of which is read by such a pushdown automaton that starts with arbitrary inner states with the empty stack and eventually reaches a unique inner state. Analogously to the Černý function for finite automata, we discuss the behaviors of the function S(n, k, e) that produces the maximal word length over all the shortest synchronizing words of n-state real-time deterministic pushdown automata with size-k stack alphabets (excluding the bottom marker) and of push size e. We prove reasonably good lower bounds and, in a certain restricted setting, upper bounds of S(n, k, e). We also study two additional variations of S(n, k, e) based on the empty- and the same-stack models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The complexity class \(\mathrm {BH}_2\) was sometimes expressed as \(\mathrm {DP}\) in the past literature and it is composed of all languages of the form \(A\cap \overline{B}\) for two languages A and B in \(\mathrm {NP}\).

  2. 2.

    We should remark that Caucal’s [1] concept of “synchronization” of pushdown automata significantly differs from our concept introduced in this exposition. Our concept is a natural extension of the synchronizing finite automata discussed in Sect. 1.1 whereas Caucal’s is obviously not.

  3. 3.

    After the technical report [5] of this paper, the decision problem of whether or not a given pushdown automaton is synchronizing has been shown to be unsolvable [3].

References

  1. Cauca D (2006) Synchronization of pushdown automata. In: Proceedings of DLT 2006, vol 4036. Springer, pp 120–132

    Google Scholar 

  2. Eppstein D (1990) Reset sequences for monotonic automata. SIAM J Comput 19:500–510

    Article  MathSciNet  Google Scholar 

  3. Fernau H, Wolf P, Yamakami T (2020) Synchronizing deterministic push-down automata can be really hard. In: Proceedings of MFCS 2020, vol 170, pp 33:1–33:15

    Google Scholar 

  4. Ginsburg S (1958) On the length of the smallest uniform experiment which distinguishes the terminal states of a machine. J ACM 5:266–280

    Article  MathSciNet  Google Scholar 

  5. Mikami E, Yamakami T (2020) Synchronizing pushdown automata and reset words. Comp2019-54(2020-03), Technical report of the institute of electronics, information and communication engineers (2020). (in Japanese)

    Google Scholar 

  6. Moore EF (1956) Gedanken-experiments on sequential machines. Autom Stud Ann Math Stud 34:129–153

    MathSciNet  Google Scholar 

  7. Olschewski J, Ummels M (2010) The complexity of finding reset words in finite automata. In: Proceedings of MFCS 2010, vol 6281. Springer, pp 568–579

    Google Scholar 

  8. Salomaa A (2002) Synchronization of finite automata: contributions to an old problem. In: Mogensen TÆ et al (ed) The essence of computation, vol 2566. Springer, pp 37–59

    Google Scholar 

  9. Shitov Y (2019) An improvement to a recent upper bound for synchronizing words of finite automata. J Aut Lang Comb 24:367–373

    MathSciNet  MATH  Google Scholar 

  10. Černý J (1964) Poznámka k homogénnym experimentom s konečnými automatami. Matematicko-fyzikálny Časopis Slovensk. Akad. Vied. 14:208–216 (in Slovak)

    Google Scholar 

  11. Černý J, Pirická A, Rosenauerová B (1971) On directable automata. Kybernetika 7:289–298

    MathSciNet  MATH  Google Scholar 

  12. Volkov MV (2008) Synchronizing automata and the Černý conjecture. In: Proceedings of LATA 2008, vol 5196. Springer, pp 11–27

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Fukui, 3-9-1 Bunkyo, Fukui, 910-8507, Japan

    Tomoyuki Yamakami & Eitatsu Mikami

Authors
  1. Tomoyuki Yamakami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eitatsu Mikami
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  2. The University of Texas at San Antonio, San Antonio, TX, USA

    Kim-Kwang Raymond Choo

  3. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

    Saminathan Ponnusamy

  4. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  5. Department of Computer Engineering, Ondokuz Mayis University, Atakum, Turkey

    Sedat Akleylek

  6. Department of Information Technology, Indian Institute of Engineering Science and Technology, West Bengal, India

    Santi Prasad Maity

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Yamakami, T., Mikami, E. (2022). Synchronizing Words for Real-Time Deterministic Pushdown Automata. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_41

Download citation

Publish with us

Policies and ethics

Search

Navigation