Proceedings of the Yerevan State University, series Physical and Mathematical Sciences
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Proceedings of the YSU, Physical and Mathematical Sciences:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Proceedings of the YSU, Physical and Mathematical Sciences, 2015, Issue 1, Pages 52–60 (Mi uzeru15)  

This article is cited in 9 scientific papers (total in 9 papers)

Informatics

On non-classical theory of computability

S. A. Nigiyan

Yerevan State University

Abstract: Definition of arithmetical functions with indeterminate values of arguments is given. Notions of computability, strong computability and $\lambda$-definability for such functions are introduced. Monotonicity and computability of every $\lambda$-definable arithmetical function with indeterminate values of arguments is proved. It is proved that every computable, naturally extended arithmetical function with indeterminate values of arguments is $\lambda$-definable. It is also proved that there exist strong computable, monotonic arithmetical functions with indeterminate values of arguments, which are not $\lambda$-definable. The $\delta$-redex problem for strong computable, monotonic arithmetical functions with indeterminate values of arguments is defined. It is proved that there exist strong computable, $\lambda$-definable arithmetical functions with indeterminate values of arguments, for which the $\delta$-redex problem is unsolvable.

Keywords: arithmetical function, indeterminate value of argument, computability, strong computability, $\lambda$-definability, $\beta$-redex, $\delta$-redex.

Full text: PDF file (162 kB)
References: PDF file   HTML file
MSC: Primary 68Q01; Secondary 68Q05
Received: 20.10.2014
Accepted:17.12.2014
Language:

Citation: S. A. Nigiyan, “On non-classical theory of computability”, Proceedings of the YSU, Physical and Mathematical Sciences, 2015, no. 1, 52–60

Citation in format AMSBIB
\Bibitem{Nig15}
\by S.~A.~Nigiyan
\paper On non-classical theory of computability
\jour Proceedings of the YSU, Physical and Mathematical Sciences
\yr 2015
\issue 1
\pages 52--60
\mathnet{http://mi.mathnet.ru/uzeru15}


Linking options:
  • http://mi.mathnet.ru/eng/uzeru15
  • http://mi.mathnet.ru/eng/uzeru/y2015/i1/p52

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. V. Khondkaryan, “On typed and untyped lambda-terms”, Uch. zapiski EGU, ser. Fizika i Matematika, 2015, no. 2, 45–52  mathnet
    2. S. A. Nigiyan, “On $\lambda$-definability of arithmetical functions with indeterminate values of arguments”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 2, 39–47  mathnet
    3. S. A. Nigiyan, T. V. Khondkaryan, “On canonical notion of $\delta$-reduction and on translation of typed $\lambda$-terms into untyped $\lambda$-terms”, Uch. zapiski EGU, ser. Fizika i Matematika, 51:1 (2017), 46–52  mathnet
    4. S. A. Nigiyan, T. V. Khondkaryan, “On translation of typed functional programs into untyped functional programs”, Uch. zapiski EGU, ser. Fizika i Matematika, 51:2 (2017), 177–186  mathnet
    5. D. A. Grigoryan, “On incomparability of interpretation algorithms of typed functional programs with respect to undefined value”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:2 (2018), 109–118  mathnet
    6. D. A. Grigoryan, “On main canonical notion of $\delta$-reduction”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:3 (2018), 191–199  mathnet
    7. L. Budaghyan, D. A. Grigoryan, L. H. Torosyan, “A necessary and sufficient condition for the uniqueness of $\beta\delta$-normal form of typed $\lambda$-terms”, Uch. zapiski EGU, ser. Fizika i Matematika, 53:1 (2019), 28–36  mathnet
    8. D. A. Grigoryan, “On the uniqueness of $\beta\delta$-normal form of typed $\lambda$-terms for the canonical notion of $\delta$-reduction”, Uch. zapiski EGU, ser. Fizika i Matematika, 53:1 (2019), 37–46  mathnet
    9. S. A. Nigiyan, “$\lambda$-definability of built-in McCarthy functions as functions with indeterminate values of arguments”, Uch. zapiski EGU, ser. Fizika i Matematika, 53:3 (2019), 191–202  mathnet
  • Proceedings of the Yerevan State University, series Physical and Mathematical Sciences
    Number of views:
    This page:168
    Full text:55
    References:72

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021