Skip to main content
SpringerLink
Log in

Minimal zero words for second-order matrices

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

An exact estimate is given for the length of a minimal zero word (sequence). This estimate equals q+2 for second-order matrices over a finite field GF(q). The correspondence problem is proved to be undecidable for matrices with rational elements.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Paterson, “Unsolvability in 3×3_matrices,” Studies in Applied Mathematics, 49, 105–107 (1970).

    MathSciNet  Google Scholar 

  2. O. Bournez and M. Branicky, “The mortality problem for matrices of low dimensions,” Theory Comput. Systems, 35, 433–448 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  3. I. K. Rystsov, “Representation of regular ideals in finite automata,” Cybernetics and Systems Analysis, No. 5, 48–58 (2003).

  4. R. Hartshorne, Fundamentals of Projective Geometry [Russian translation], Mir, Moscow (1970).

    Google Scholar 

  5. A. A. Albert, “Finite fields,” Kibern. Sb., No. 3, 7–49 (1966).

  6. G. Galperin and A. Zemlyakov, Mathematical Billiards [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  7. A. Salomaa, Pearls of Formal Language Theory [Russian translation], Mir, Moscow (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Technical University of Ukraine “Kiev Polytechnic Institute”, Kiev, Ukraine

    I. K. Rystsov

Authors
  1. I. K. Rystsov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 10–18, July–August 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rystsov, I.K. Minimal zero words for second-order matrices. Cybern Syst Anal 43, 478–483 (2007). https://doi.org/10.1007/s10559-007-0074-2

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-007-0074-2

Keywords

Search

Navigation