Skip to main content
SpringerLink
Log in

Unambiguity and Fewness for Nonuniform Families of Polynomial-Size Nondeterministic Finite Automata

  • Conference paper
  • First Online:
Reachability Problems (RP 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13608))

Included in the following conference series:

Abstract

Nonuniform families of polynomial-size finite automata, which are series of indexed finite automata having polynomially many inner states, are used in the past literature to solve nonuniform families of promise decision problems. In such a nonuniform family, we focus our attention, in particular, on the variants of nondeterministic finite automata, which have at most “one” (unique or unambiguous), “polynomially many” (few) accepting computation paths, or unique/few computation paths leading to each fixed configuration. We prove that those variants of one-way machines are different in computational power. As for two-way machines restricted to instances of polynomially-bounded size, families of two-way polynomial-size nondeterministic finite automata are equivalent in power to families of unambiguous finite automata.

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 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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.

    This notion is called just “few” in [12]. For clarity reason, here we use a slightly different term.

References

  1. Allender, E.W.: The complexity of sparse sets in P. In: Selman, A.L. (ed.) Structure in Complexity Theory. LNCS, vol. 223, pp. 1–11. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-16486-3_85

    Chapter  Google Scholar 

  2. Allender, E., Rubinstein, R.: P-printable sets. SIAM J. Comput. 17, 1193–1202 (1988)

    Article  MathSciNet  Google Scholar 

  3. Berman P., Lingas, A.: On complexity of regular languages in terms of finite automata, Report 304, Institute of Computer Science, Polish Academy of Science, Warsaw (1977)

    Google Scholar 

  4. Bourke, C., Tewari, R., Vinodchandran, N.V.: Directed planar reachability is in unambiguous log-space. ACM Trans. Comput. Theory 1, 1–17 (2009)

    Article  Google Scholar 

  5. Buntrock, G., Jenner, B., Lange, K., Rossmanith, P.: Unambiguity and fewness for logarithmic space. In: the Proceedings of FCT1991, LNCS vol. 529, pp. 168–179 (1991)

    Google Scholar 

  6. Kapoutsis, C.A.: Size complexity of two-way finite automata. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 47–66. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02737-6_4

    Chapter  Google Scholar 

  7. Kapoutsis, C.A.: Minicomplexity. J. Automat. Lang. Combin. 17, 205–224 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Kapoutsis, C.A.: Two-way automata versus logarithmic space. Theory Comput. Syst. 55, 421–447 (2014)

    Article  MathSciNet  Google Scholar 

  9. Kapoutsis, C.A., Pighizzini, G.: Two-way automata characterizations of L/poly versus NL. Theory Comput. Syst. 56, 662–685 (2015)

    Google Scholar 

  10. Karp, R.M., Lipton, R.J.: Tring machines that take advice. L’Enseigrement Mathématique 28, 191–209 (1982)

    MATH  Google Scholar 

  11. Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Third edition. Springer, Cham (2008). https://doi.org/10.1007/978-0-387-49820-1

  12. Pavan, A., Tewari, R., Vinodchandran, N.V.: On the power of unambiguity in logspace. Comput. Complex. 21, 643–670 (2012)

    Article  Google Scholar 

  13. Reinhardt, K., Allender, E.: Making nondeterminism unambiguous. SIAM J. Comput. 29, 1118–1131 (2000)

    Article  MathSciNet  Google Scholar 

  14. Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two-way finite automata. In: the Proceedings of STOC 1978, pp. 275–286 (1978)

    Google Scholar 

  15. Valiant, L.: The relative complexity of checking and evaluating. Inf. Process. Lett. 5, 20–23 (1976)

    Article  MathSciNet  Google Scholar 

  16. Yamakami, T.: The 2CNF Boolean formula satisfiability problem and the linear space hypothesis. In: the Proceedings of MFCS 2017, LIPIcs, vol. 83, 1–14 (2017). arXiv preprint arXiv:1709.10453

  17. Yamakami, T.: State complexity characterizations of parameterized degree-bounded graph connectivity, sub-linear space computation, and the linear space hypothesis. Theor. Comput. Sci. 798, 2–22 (2019)

    Article  MathSciNet  Google Scholar 

  18. Yamakami, T.: Nonuniform families of polynomial-size quantum finite automata and quantum logarithmic-space computation with polynomial-size advice. Inform. Comput. 286, 104783 (2022). A preliminary version appeared in the Proceedings of LATA 2019, LNCS, vol. 11417, pp. 134–145 (2019)

    Google Scholar 

  19. Yamakami, T.: Relativizations of nonuniform quantum finite automata families. In: the Proceedings of UCNC 2019, LNCS, vol. 11493, pp. 257–271 (2019)

    Google Scholar 

  20. Yamakami, T.: Parameterizations of logarithmic-space reductions, stack-state complexity of nonuniform families of pushdown automata, and a road to the LOGCFL\(\subseteq \)LOGDCFL/poly question. arXiv preprint arXiv:2108.12779 (2021)

Download references

Author information

Authors and Affiliations

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

    Tomoyuki Yamakami

Authors
  1. Tomoyuki Yamakami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomoyuki Yamakami .

Editor information

Editors and Affiliations

  1. Department of Computer Science, TU Kaiserslautern, Kaiserslautern, Germany

    Anthony W. Lin

  2. Max Planck Institute for Software Systems, Kaiserslautern, Germany

    Georg Zetzsche

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Yamakami, T. (2022). Unambiguity and Fewness for Nonuniform Families of Polynomial-Size Nondeterministic Finite Automata. In: Lin, A.W., Zetzsche, G., Potapov, I. (eds) Reachability Problems. RP 2022. Lecture Notes in Computer Science, vol 13608. Springer, Cham. https://doi.org/10.1007/978-3-031-19135-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-19135-0_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-19134-3

  • Online ISBN: 978-3-031-19135-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation