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Documents authored by Nakano, Keisuke


Document
Idempotent Turing Machines

Authors: Keisuke Nakano

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
A function f is said to be idempotent if f(f(x)) = f(x) holds whenever f(x) is defined. This paper presents a computation model for idempotent functions, called an idempotent Turing machine. The computation model is necessarily and sufficiently expressive in the sense that not only does it always compute an idempotent function but also every idempotent computable function can be computed by an idempotent Turing machine. Furthermore, a few typical properties of the computation model such as robustness and universality are shown. Our computation model is expected to be a basis of special-purpose (or domain-specific) programming languages in which only but all idempotent computable functions can be defined.

Cite as

Keisuke Nakano. Idempotent Turing Machines. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 79:1-79:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{nakano:LIPIcs.MFCS.2021.79,
  author =	{Nakano, Keisuke},
  title =	{{Idempotent Turing Machines}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{79:1--79:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.79},
  URN =		{urn:nbn:de:0030-drops-145191},
  doi =		{10.4230/LIPIcs.MFCS.2021.79},
  annote =	{Keywords: Turing machines, Idempotent functions, Computable functions, Computation model}
}
Document
On Repetitive Right Application of B-Terms

Authors: Mirai Ikebuchi and Keisuke Nakano

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)


Abstract
B-terms are built from the B combinator alone defined by B == lambda f.lambda g.lambda x. f~(g~x), which is well-known as a function composition operator. This paper investigates an interesting property of B-terms, that is, whether repetitive right applications of a B-term cycles or not. We discuss conditions for B-terms to have and not to have the property through a sound and complete equational axiomatization. Specifically, we give examples of B-terms which have the property and show that there are infinitely many B-terms which do not have the property. Also, we introduce a canonical representation of B-terms that is useful to detect cycles, or equivalently, to prove the property, with an efficient algorithm.

Cite as

Mirai Ikebuchi and Keisuke Nakano. On Repetitive Right Application of B-Terms. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{ikebuchi_et_al:LIPIcs.FSCD.2018.18,
  author =	{Ikebuchi, Mirai and Nakano, Keisuke},
  title =	{{On Repetitive Right Application of B-Terms}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.18},
  URN =		{urn:nbn:de:0030-drops-91882},
  doi =		{10.4230/LIPIcs.FSCD.2018.18},
  annote =	{Keywords: Combinatory logic, B combinator, Lambda calculus}
}
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