Continuous and monotone machines

Michal Konečný, Florian Steinberg, Holger Thies

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

1 被引用数 (Scopus)

抄録

We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that it is possible to translate back and forth between such machines and names in the standard function encoding used in computable analysis. Put differently, among the operators on Baire space, exactly the partial continuous ones are implementable by continuous machines and the data that such a machine provides is a description of the operator as a sequentially realizable functional. Continuous machines are naturally formulated in type theories and we have formalized our findings in Coq as part of Incone, a Coq library for computable analysis. The correctness proofs use a classical meta-theory with countable choice. Along the way we formally prove some known results such as the existence of a self-modulating modulus of continuity for partial continuous operators on Baire space. To illustrate their versatility we use continuous machines to specify some algorithms that operate on objects that cannot be fully described by finite means, such as real numbers and functions. We present particularly simple algorithms for finding the multiplicative inverse of a real number and for composition of partial continuous operators on Baire space. Some of the simplicity is achieved by utilizing the fact that continuous machines are compatible with multivalued semantics.

本文言語英語
ホスト出版物のタイトル45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020
編集者Javier Esparza, Daniel Kral�, Daniel Kral�
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(電子版)9783959771597
DOI
出版ステータス出版済み - 8月 1 2020
イベント45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020 - Prague, チェコ共和国
継続期間: 8月 25 20208月 26 2020

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
170
ISSN(印刷版)1868-8969

会議

会議45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020
国/地域チェコ共和国
CityPrague
Period8/25/208/26/20

!!!All Science Journal Classification (ASJC) codes

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