Computation Universality of One-Dimensional Reversible (Injective) Cellular Automata
The Transactions of the IEICE Volume E72 Issue 6
Page 758-762
published_at 1989-06-25
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| File | |
| Title ( eng ) |
Computation Universality of One-Dimensional Reversible (Injective) Cellular Automata
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| Creator |
Harao Masateru
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| Source Title |
The Transactions of the IEICE
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| Volume | E72 |
| Issue | 6 |
| Start Page | 758 |
| End Page | 762 |
| Abstract |
A reversible cellular automaton (CA) is a "backward deterministic" CA, i.e, every configuration of it has at most one predecessor. Toffoli showed that a two-dimensional reversible cellular automaton is computation universal. He posed an open problem whether a one-dimensional reversible CA is computation universal. In this paper, we solve this problem affirmatively. This result is proved by using the previous result of Morita et al. that a 1-tape reversible Turing machine is computation universal. We give a construction method of a reversible CA which simulates a given 1-tape reversible Turing machine. To do this, we introduce a "one-dimensional partitioned cellular automaton" (1-PCA). 1-PCA has the property that the local reversibility (i.e., injectivity of a local function) is equivalent to the global reversibility, and thus it facilitates to design a reversible CA.
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| Keywords |
reversible computing
cellular automata
computational universality
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
電子情報通信学会
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| Date of Issued | 1989-06-25 |
| Rights |
Copyright (c) 1989 IEICE
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| Publish Type | Version of Record |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0913-574X
[NCID] AA10684666
[URI] https://search.ieice.org/bin/summary.php?id=e72-e_6_758&category=E&lang=E&year=1989&abst=
[URI] https://search.ieice.org/
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