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

Proceedings of the Yerevan State University, series Physical and Mathematical Sciences

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Proceedings of the Yerevan State University, series 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

Full-text PDF (162 kB) Citations (9)

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Abstract: Definition of arithmetical functions with indeterminate values of arguments is given. Notions of computability, strong computability and

λ

$\lambda$ -definability for such functions are introduced. Monotonicity and computability of every

λ

$\lambda$ -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

λ

$\lambda$ -definable. It is also proved that there exist strong computable, monotonic arithmetical functions with indeterminate values of arguments, which are not

λ

$\lambda$ -definable. The

δ

$\delta$ -redex problem for strong computable, monotonic arithmetical functions with indeterminate values of arguments is defined. It is proved that there exist strong computable,

λ

$\lambda$ -definable arithmetical functions with indeterminate values of arguments, for which the

δ

$\delta$ -redex problem is unsolvable.

Keywords: arithmetical function, indeterminate value of argument, computability, strong computability,

λ

$\lambda$ -definability,

β

$\beta$ -redex,

δ

$\delta$ -redex.

Received: 20.10.2014
Accepted: 17.12.2014

Document Type: Article

MSC: Primary 68Q01; Secondary 68Q05

Language: English

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:

https://www.mathnet.ru/eng/uzeru15

https://www.mathnet.ru/eng/uzeru/y2015/i1/p52

This publication is cited in the following 9 articles:

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
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
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
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
D. A. Grigoryan, “On main canonical notion of $\delta$ -reduction”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:3 (2018), 191–199
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
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
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
T. V. Khondkaryan, “On typed and untyped lambda-terms”, Uch. zapiski EGU, ser. Fizika i Matematika, 2015, no. 2, 45–52

Citing articles in Google Scholar: Russian citations, English citations
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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences

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