更改

此词条暂由彩云小译翻译，翻译字数共2516，未经人工整理和审校，带来阅读不便，请见谅。

此词条暂由彩云小译翻译，翻译字数共2516，未经人工整理和审校，带来阅读不便，请见谅。

{{Short description|Self replicating cellular automata}}

{{Short description|Self replicating cellular automata}}

[[Image:Nobili Pesavento 2reps.png|right|thumb|400px|The first implementation of von Neumann's self-reproducing universal constructor.<ref name=Pesavento1995>{{Citation|journal=Artificial Life| title=An implementation of von Neumann's self-reproducing machine| year=1995| first=Umberto| last=Pesavento|volume=2|issue=4|pages=337–354|publisher=MIT Press|url=http://dragonfly.tam.cornell.edu/~pesavent/pesavento_self_reproducing_machine.pdf|archive-url=https://web.archive.org/web/20070621164824/http://dragonfly.tam.cornell.edu/~pesavent/pesavento_self_reproducing_machine.pdf |archive-date=June 21, 2007 |doi=10.1162/artl.1995.2.337|pmid=8942052}}</ref> Three generations of machine are shown: the second has nearly finished constructing the third. The lines running to the right are the tapes of genetic instructions, which are copied along with the body of the machines. The machine shown runs in a 32-state version of von Neumann's cellular automata environment, not his original 29-state specification.]]

[[Image:Nobili Pesavento 2reps.png|right|thumb|400px|The first implementation of von Neumann's self-reproducing universal constructor.<ref name=Pesavento1995>{{Citation|journal=Artificial Life| title=An implementation of von Neumann's self-reproducing machine| year=1995| first=Umberto| last=Pesavento|volume=2|issue=4|pages=337–354|publisher=MIT Press|url=http://dragonfly.tam.cornell.edu/~pesavent/pesavento_self_reproducing_machine.pdf|archive-url=https://web.archive.org/web/20070621164824/http://dragonfly.tam.cornell.edu/~pesavent/pesavento_self_reproducing_machine.pdf |archive-date=June 21, 2007 |doi=10.1162/artl.1995.2.337|pmid=8942052}}</ref> Three generations of machine are shown: the second has nearly finished constructing the third. The lines running to the right are the tapes of genetic instructions, which are copied along with the body of the machines. The machine shown runs in a 32-state version of von Neumann's cellular automata environment, not his original 29-state specification.

 

右 | 拇指 | 400px | 冯 · 诺依曼的自复制通用构造函数的第一个实现。三代机器显示: 第二个已经接近完成建设第三。右边的线条是遗传指令的磁带，这些磁带随着机器的身体一起被复制。所展示的机器运行在32状态的冯 · 诺依曼的细胞自动机环境中，而不是他最初的29状态规范。

冯 · 诺依曼的自复制通用构造函数的第一个实现。三代机器显示: 第二个已经接近完成建设第三。右边的线条是遗传指令的磁带，这些磁带随着机器的身体一起被复制。所展示的机器运行在32状态的冯 · 诺依曼的细胞自动机环境中，而不是他最初的29状态规范。]]

[[John von Neumann]]'s '''universal constructor''' is a [[self-replicating machine]] in a [[cellular automata]] (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book ''Theory of Self-Reproducing Automata'', completed in 1966 by [[Arthur Burks|Arthur W. Burks]] after von Neumann's death.<ref name=TSRA>{{Citation| url=https://archive.org/details/theoryofselfrepr00vonn_0| title=''Theory of Self-Reproducing Automata.''| author1=von Neumann, John| author2=Burks, Arthur W.| year=1966| publisher=University of Illinois Press| format=Scanned book online| archive-date=2015-06-24| access-date=2017-02-28}}</ref> While typically not as well known as von Neumann's other work, it is regarded as foundational for [[automata theory]], [[complex systems]], and [[artificial life]].<ref name=McMullin2000>{{Citation|journal=Artificial Life|last=McMullin|first=B.|year=2000|title=John von Neumann and the Evolutionary Growth of Complexity: Looking Backwards, Looking Forwards...|volume=6|issue=4|pages=347–361|url=http://www.eeng.dcu.ie/~alife/bmcm-alj-2000/|doi=10.1162/106454600300103674|pmid=11348586|s2cid=5454783}}</ref><ref name=Rocha1998>{{Citation|journal=Evolutionary Systems| title=Selected self-organization and the semiotics of evolutionary systems| year=1998| first=Luis M.| last=Rocha|pages=341–358|publisher=Springer, Dordrecht| doi=10.1007/978-94-017-1510-2_25| isbn=978-90-481-5103-5|url=https://link.springer.com/chapter/10.1007/978-94-017-1510-2_25}}</ref> Indeed, Nobel Laureate [[Sydney Brenner]] considered Von Neumann's work on self-reproducing automata (together with [[Turing]]'s work on computing machines) central to [[biological theory]] as well, allowing us to "discipline our thoughts about machines, both natural and artificial."<ref name=Brenner2012>{{Citation|journal=Nature| title=Life's code script| year=2012| first=Sydney| last=Brenner|volume=482| issue=7386|pages=461|url=https://www.nature.com/articles/482461a|doi=10.1038/482461a|pmid=22358811| s2cid=205070101}}</ref>

[[John von Neumann]]'s '''universal constructor''' is a [[self-replicating machine]] in a [[cellular automata]] (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book ''Theory of Self-Reproducing Automata'', completed in 1966 by [[Arthur Burks|Arthur W. Burks]] after von Neumann's death.<ref name=TSRA>{{Citation| url=https://archive.org/details/theoryofselfrepr00vonn_0| title=''Theory of Self-Reproducing Automata.''| author1=von Neumann, John| author2=Burks, Arthur W.| year=1966| publisher=University of Illinois Press| format=Scanned book online| archive-date=2015-06-24| access-date=2017-02-28}}</ref> While typically not as well known as von Neumann's other work, it is regarded as foundational for [[automata theory]], [[complex systems]], and [[artificial life]].<ref name=McMullin2000>{{Citation|journal=Artificial Life|last=McMullin|first=B.|year=2000|title=John von Neumann and the Evolutionary Growth of Complexity: Looking Backwards, Looking Forwards...|volume=6|issue=4|pages=347–361|url=http://www.eeng.dcu.ie/~alife/bmcm-alj-2000/|doi=10.1162/106454600300103674|pmid=11348586|s2cid=5454783}}</ref><ref name=Rocha1998>{{Citation|journal=Evolutionary Systems| title=Selected self-organization and the semiotics of evolutionary systems| year=1998| first=Luis M.| last=Rocha|pages=341–358|publisher=Springer, Dordrecht| doi=10.1007/978-94-017-1510-2_25| isbn=978-90-481-5103-5|url=https://link.springer.com/chapter/10.1007/978-94-017-1510-2_25}}</ref> Indeed, Nobel Laureate [[Sydney Brenner]] considered Von Neumann's work on self-reproducing automata (together with [[Turing]]'s work on computing machines) central to [[biological theory]] as well, allowing us to "discipline our thoughts about machines, both natural and artificial."<ref name=Brenner2012>{{Citation|journal=Nature| title=Life's code script| year=2012| first=Sydney| last=Brenner|volume=482| issue=7386|pages=461|url=https://www.nature.com/articles/482461a|doi=10.1038/482461a|pmid=22358811| s2cid=205070101}}</ref>

John von Neumann's universal constructor is a self-replicating machine in a cellular automata (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book Theory of Self-Reproducing Automata, completed in 1966 by Arthur W. Burks after von Neumann's death. While typically not as well known as von Neumann's other work, it is regarded as foundational for automata theory, complex systems, and artificial life. Indeed, Nobel Laureate Sydney Brenner considered Von Neumann's work on self-reproducing automata (together with Turing's work on computing machines) central to biological theory as well, allowing us to "discipline our thoughts about machines, both natural and artificial."

John von Neumann's universal constructor is a self-replicating machine in a cellular automata (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book Theory of Self-Reproducing Automata, completed in 1966 by Arthur W. Burks after von Neumann's death. While typically not as well known as von Neumann's other work, it is regarded as foundational for automata theory, complex systems, and artificial life. Indeed, Nobel Laureate Sydney Brenner considered Von Neumann's work on self-reproducing automata (together with Turing's work on computing machines) central to biological theory as well, allowing us to "discipline our thoughts about machines, both natural and artificial."

约翰·冯·诺伊曼的通用构造器是细胞自动机(CA)环境中的自我复制机械。它是在20世纪40年代设计的，当时没有使用计算机。机器的基本细节发表在冯 · 诺依曼的《自复制自动机理论》一书中，该书由冯 · 诺依曼死后的亚瑟 · w · 伯克斯于1966年完成。虽然通常不像冯 · 诺依曼的其他著作那样广为人知，但它被认为是自动机理论、复杂系统和人工生命的基础。事实上，诺贝尔奖获得者悉尼 · 布伦纳认为冯 · 诺依曼关于自我复制自动机的工作(以及图灵关于计算机的工作)对生物学理论同样重要，它允许我们“约束我们关于自然和人工机器的思想”

约翰·冯·诺伊曼的通用构造器是细胞自动机(CA)环境中的自我复制机械。它是在20世纪40年代设计的，当时没有使用计算机。机器的基本细节发表在冯 · 诺依曼的《自复制自动机理论》一书中，该书由冯 · 诺依曼死后的亚瑟 · w · 伯克斯于1966年完成。虽然通常不像冯 · 诺依曼的其他著作那样广为人知，但它被认为是自动机理论、复杂系统和人工生命的基础。事实上，诺贝尔奖获得者悉尼 · 布伦纳认为冯 · 诺依曼关于自我复制自动机的工作(以及图灵关于计算机的工作)对生物学理论同样重要，它允许我们“约束我们关于自然和人工机器的思想”。

Von Neumann's goal, as specified in his lectures at the University of Illinois in 1949,<ref name="TSRA"/> was to design a machine whose complexity could grow automatically akin to biological organisms under [[Natural Selection|natural selection]]. He asked what is the ''threshold of complexity'' that must be crossed for machines to be able to evolve.<ref name=Rocha1998/> His answer was to specify an abstract machine which, when run, would replicate itself. In his design, the self-replicating machine consists of three parts: a "description" of ('blueprint' or program for) itself, a ''universal constructor'' mechanism that can read any description and construct the machine (sans description) encoded in that description, and a ''universal copy machine'' that can make copies of any description. After the universal constructor has been used to construct a new machine encoded in the description, the copy machine is used to create a copy of that description, and this copy is passed on to the new machine, resulting in a working replication of the original machine that can keep on reproducing. Some machines will do this backwards, copying the description and then building a machine. Crucially, the self-reproducing machine can evolve by accumulating mutations of the description, not the machine itself, thus gaining the ability to grow in complexity.<ref name=Rocha1998/><ref name=Brenner2012/>

Von Neumann's goal, as specified in his lectures at the University of Illinois in 1949,<ref name="TSRA"/> was to design a machine whose complexity could grow automatically akin to biological organisms under [[Natural Selection|natural selection]]. He asked what is the ''threshold of complexity'' that must be crossed for machines to be able to evolve.<ref name=Rocha1998/> His answer was to specify an abstract machine which, when run, would replicate itself. In his design, the self-replicating machine consists of three parts: a "description" of ('blueprint' or program for) itself, a ''universal constructor'' mechanism that can read any description and construct the machine (sans description) encoded in that description, and a ''universal copy machine'' that can make copies of any description. After the universal constructor has been used to construct a new machine encoded in the description, the copy machine is used to create a copy of that description, and this copy is passed on to the new machine, resulting in a working replication of the original machine that can keep on reproducing. Some machines will do this backwards, copying the description and then building a machine. Crucially, the self-reproducing machine can evolve by accumulating mutations of the description, not the machine itself, thus gaining the ability to grow in complexity.<ref name=Rocha1998/><ref name=Brenner2012/>

== Purpose ==

== Purpose ==

== Purpose ==

= 目的  =  

[[File:Von Neuman Self-replication 2.jpg|thumb|400px|right|Von Neumann's System of Self-Replication Automata with the ability to evolve (Figure adapted from [[Luis M. Rocha|Luis Rocha]]'s Lecture Notes at Indiana University<ref name=Rocha_lec_notes>{{citation |last=Rocha|first=Luis M.| year=2015 |title=Lecture Notes of I-485-Biologically Inspired Computing Course, Indiana University|chapter=Chapter 6. Von Neumann and Natural Selection.|chapter-url=https://homes.luddy.indiana.edu/rocha/academics/i-bic/pdfs/ibic_lecnotes_c6.pdf|url=https://homes.luddy.indiana.edu/rocha/academics/i-bic/pdfs/ibic_lecnotes.pdf}}</ref>). i) the self-replicating system is composed of several automata plus a separate description (an encoding formalized as a [[Turing Machine|Turing 'tape']]) of all the automata: Universal Constructor (A), Universal Copier (B), Operating System (C), extra functions not involved with replication (D), and separate description Φ(A,B,C,D) encoding all automata. ii) (Top) Universal Constructor produces (decodes) automata from their description (''active'' mode of description); (Bottom) Universal Copier copies description of automata (''passive'' mode of description); Mutations Φ(D') to description Φ(D) (not changes in automaton D directly) propagate to the set of automata produced in next generation, allowing (automata + description) system to continue replicating and evolving (D → D').<ref name=Rocha1998/> The active process of construction from a description parallels [[Translation (biology)|DNA translation]], the passive process of copying the description parallels [[DNA replication]], and inheritance of mutated descriptions parallels [[Mutation|Vertical inheritance of DNA mutations]] in Biology,<ref name=Rocha1998/><ref name=Brenner2012/> and were proposed by Von Neumann before the discovery of the structure of the DNA molecule and how it is separately translated and replicated in the Cell.<ref name=Rocha_lec_notes/>|链接=Special:FilePath/Von_Neuman_Self-replication_2.jpg]]

 

[[File:Von Neuman Self-replication 2.jpg|thumb|400px|right|Von Neumann's System of Self-Replication Automata with the ability to evolve (Figure adapted from [[Luis M. Rocha|Luis Rocha]]'s Lecture Notes at Indiana University<ref name=Rocha_lec_notes>{{citation |last=Rocha|first=Luis M.| year=2015 |title=Lecture Notes of I-485-Biologically Inspired Computing Course, Indiana University|chapter=Chapter 6. Von Neumann and Natural Selection.|chapter-url=https://homes.luddy.indiana.edu/rocha/academics/i-bic/pdfs/ibic_lecnotes_c6.pdf|url=https://homes.luddy.indiana.edu/rocha/academics/i-bic/pdfs/ibic_lecnotes.pdf}}</ref>). i) the self-replicating system is composed of several automata plus a separate description (an encoding formalized as a [[Turing Machine|Turing 'tape']]) of all the automata: Universal Constructor (A), Universal Copier (B), Operating System (C), extra functions not involved with replication (D), and separate description Φ(A,B,C,D) encoding all automata. ii) (Top) Universal Constructor produces (decodes) automata from their description (''active'' mode of description); (Bottom) Universal Copier copies description of automata (''passive'' mode of description); Mutations Φ(D') to description Φ(D) (not changes in automaton D directly) propagate to the set of automata produced in next generation, allowing (automata + description) system to continue replicating and evolving (D → D').<ref name=Rocha1998/> The active process of construction from a description parallels [[Translation (biology)|DNA translation]], the passive process of copying the description parallels [[DNA replication]], and inheritance of mutated descriptions parallels [[Mutation|Vertical inheritance of DNA mutations]] in Biology,<ref name=Rocha1998/><ref name=Brenner2012/> and were proposed by Von Neumann before the discovery of the structure of the DNA molecule and how it is separately translated and replicated in the Cell.<ref name=Rocha_lec_notes/>]]

Von Neumann's design has traditionally been understood to be a demonstration of the logical requirements for machine self-replication.<ref name=McMullin2000/> However, it is clear that far simpler machines can achieve self-replication. Examples include trivial [[Crystal growth|crystal-like growth]], [[template replication]], and [[Langton's loops]]. But von Neumann was interested in something more profound: construction, universality, and evolution.<ref name=Rocha1998/><ref name=Brenner2012/>

Von Neumann's design has traditionally been understood to be a demonstration of the logical requirements for machine self-replication.<ref name=McMullin2000/> However, it is clear that far simpler machines can achieve self-replication. Examples include trivial [[Crystal growth|crystal-like growth]], [[template replication]], and [[Langton's loops]]. But von Neumann was interested in something more profound: construction, universality, and evolution.<ref name=Rocha1998/><ref name=Brenner2012/>

在实践中，当我们考虑冯 · 诺依曼所追求的特定自动机实现时，我们得出结论，它不会产生太多的进化动力学，因为机器太脆弱了——绝大多数的扰动会导致它们有效地解体。因此，他在伊利诺伊州的演讲中概述的概念模型是今天人们更感兴趣的，因为它展示了机器原则上是如何进化的。这个发现更加引人注目，因为这个模型是在上面讨论的 DNA 分子结构被发现之前。值得注意的是，Von Neumann 的设计认为向着更高复杂性的突变需要发生在(描述)子系统中，而这些子系统本身并不涉及自我复制，这是由额外的自动机 d 来概念化的，他认为这些自动机执行所有不直接涉及复制的功能(见上面的图和 Von Neumann 的具有进化能力的自我复制自动机系统)事实上，在生物有机体中，只观察到遗传密码的微小变异，这与冯 · 诺依曼的理论基础相符，即通用构造器(a)和复印器(b)本身不会进化，将所有进化(和复杂性的增长)留给自动机 d。在他未完成的著作中，冯 · 诺依曼还简要地考虑了他的自我繁殖机器之间的冲突和相互作用，以便从他的自我繁殖机器理论中理解生态和社会相互作用的进化。

在实践中，当我们考虑冯 · 诺依曼所追求的特定自动机实现时，我们得出结论，它不会产生太多的进化动力学，因为机器太脆弱了——绝大多数的扰动会导致它们有效地解体。因此，他在伊利诺伊州的演讲中概述的概念模型是今天人们更感兴趣的，因为它展示了机器原则上是如何进化的。这个发现更加引人注目，因为这个模型是在上面讨论的 DNA 分子结构被发现之前。值得注意的是，Von Neumann 的设计认为向着更高复杂性的突变需要发生在(描述)子系统中，而这些子系统本身并不涉及自我复制，这是由额外的自动机 d 来概念化的，他认为这些自动机执行所有不直接涉及复制的功能(见上面的图和 Von Neumann 的具有进化能力的自我复制自动机系统)事实上，在生物有机体中，只观察到遗传密码的微小变异，这与冯 · 诺依曼的理论基础相符，即通用构造器(a)和复印器(b)本身不会进化，将所有进化(和复杂性的增长)留给自动机 d。在他未完成的著作中，冯 · 诺依曼还简要地考虑了他的自我繁殖机器之间的冲突和相互作用，以便从他的自我繁殖机器理论中理解生态和社会相互作用的进化。

[[Image:Pesavento replicator inherited mutations.png|thumb|center|700px|A demonstration of the ability of von Neumann's machine to support inheritable mutations. (1) At an earlier timestep, a mutation was manually added to the second generation machine's tape. (2) Later generations both display the [[phenotype]] of the mutation (a drawing of a flower) and pass the mutation on to their children, since the tape is copied each time. This example illustrates how von Neumann's design allows for complexity growth (in theory) since the tape could specify a machine that is more complex than the one making it.]]

[[Image:Pesavento replicator inherited mutations.png|thumb|center|700px|A demonstration of the ability of von Neumann's machine to support inheritable mutations. (1) At an earlier timestep, a mutation was manually added to the second generation machine's tape. (2) Later generations both display the [[phenotype]] of the mutation (a drawing of a flower) and pass the mutation on to their children, since the tape is copied each time. This example illustrates how von Neumann's design allows for complexity growth (in theory) since the tape could specify a machine that is more complex than the one making it.|链接=Special:FilePath/Pesavento_replicator_inherited_mutations.png]]

 

== Implementations ==

== Implementations ==

C. L. Nehaniv in 2002, and also Y. Takada et al. in 2004, proposed a universal constructor directly implemented upon an asynchronous cellular automaton, rather than upon a synchronous cellular automaton.

C. L. Nehaniv in 2002, and also Y. Takada et al. in 2004, proposed a universal constructor directly implemented upon an asynchronous cellular automaton, rather than upon a synchronous cellular automaton.

2002年，c. l. Nehaniv，还有 y. Takada 等人。2004年，提出了一个通用构造函数，它直接在异步细胞自动机上实现，而不是在同步细胞自动机上实现。

2002年，c. l. Nehaniv，还有 y. Takada 等人。2004年，提出了一个通用构造函数，它直接在异步细胞自动机上实现，而不是在同步细胞自动机上实现。

|  || Nobili 32-state || 97 × 170 || 6,329 || 145,315 || 22.96 || 6.341010 ||  || 5 bits || binary || holistic constructor ||  || linear

|  || Nobili 32-state || 97 × 170 || 6,329 || 145,315 || 22.96 || 6.341010 ||  || 5 bits || binary || holistic constructor ||  || linear

|-

|-

!2007 | SR ccn/ap.EVN | | Nobili 32-state | | 97 × 100 | | 5,313 | | 56,325 | | 10.60 | | 9.59109 | | 行程长度有限的编码 | | 5位构造函数 | 二进制 | 整体 | | | | 超线性 | ！巴克利，2008 | codon5.rle | Nobili 32-state | | 112 × 50 | | 3,343 | | 44,155 | | 13.21 | | 5.87109 | | 自动收回 | 5位 | 二进制 | | 整体 | | | | | 线性 |-！29-state | 312 × 132 | | | 18,589 | | 294,844 | | 15.86 | | 2.611011 | 自动回缩 | 5位 | 二进制 | 整体 | | | | | 线性 |-！巴克利，2008 | codon4.rle | Nobili 32-state | | 109 × 59 | | 3,574 | | 37,780 | | 10.57 | | 4.31109 | | 自动回缩/位生成 | 4位 | 二进制 | 整体构造函数 | | | | | | | 线性 |-！巴克利，2009 | codon3.rle | Nobili 32-state | | 116 × 95 | | 4,855 | | 23,577 | | 4.86 | | 1.63109 | | | 自动收回/位生成/代码覆盖 | 3位 | | 二进制 | | 整体构造函数 | | | | | | | 超线性 |-！29-state | 2063 × 377 | | 264,321 | | | | | | | | | | | ≈1.121014 | | | 4位 | 二进制 | 部分构造函数 | | | | | | | | 线性 |-！2012 | phi9.rle | | Nobili 32-state | 122 × 60 | | 3957 | | 8920 | | 2.25 | | | | | 自动收缩/比特生成/代码覆盖/运行长度有限 | | 3 + 位 | | 整体构造函数 | | | | | | 超线性 | }

!2007 | <nowiki>SR ccn/ap.EVN | | Nobili 32-state | | 97 × 100 | | 5,313 | | 56,325 | | 10.60 | | 9.59109 | | 行程长度有限的编码 | | 5位构造函数 | 二进制 | 整体 | | | | 超线性 | ！巴克利，2008 | codon5.rle | Nobili 32-state | | 112 × 50 | | 3,343 | | 44,155 | | 13.21 | | 5.87109 | | 自动收回 | 5位 | 二进制 | | 整体 | | | | | 线性 |-！29-state | 312 × 132 | | | 18,589 | | 294,844 | | 15.86 | | 2.611011 | 自动回缩 | 5位 | 二进制 | 整体 | | | | | 线性 |-！巴克利，2008 | codon4.rle | Nobili 32-state | | 109 × 59 | | 3,574 | | 37,780 | | 10.57 | | 4.31109 | | 自动回缩/位生成 | 4位 | 二进制 | 整体构造函数 | | | | | | | 线性 |-！巴克利，2009 | codon3.rle | Nobili 32-state | | 116 × 95 | | 4,855 | | 23,577 | | 4.86 | | 1.63109 | | | 自动收回/位生成/代码覆盖 | 3位 | | 二进制 | | 整体构造函数 | | | | | | | 超线性 |-！29-state | 2063 × 377 | | 264,321 | | | | | | | | | | | ≈1.121014 | | | 4位 | 二进制 | 部分构造函数 | | | | | | | | 线性 |-！2012 | phi9.rle | | Nobili 32-state | 122 × 60 | | 3957 | | 8920 | | 2.25 | | | | | 自动收缩/比特生成/代码覆盖/运行长度有限 | | 3 + 位 | | 整体构造函数 | | | | | | 超线性 | }</nowiki>

As defined by von Neumann, universal construction entails the construction of passive configurations, only. As such, the concept of universal construction constituted nothing more than a literary (or, in this case, mathematical) device. It facilitated other proof, such as that a machine well constructed may engage in self-replication, while universal construction itself was simply assumed over a most minimal case. Universal construction under this standard is trivial. Hence, while all the configurations given here can construct any passive configuration, none can construct the real-time crossing organ devised by Gorman.<ref name="Automata2008"/>

As defined by von Neumann, universal construction entails the construction of passive configurations, only. As such, the concept of universal construction constituted nothing more than a literary (or, in this case, mathematical) device. It facilitated other proof, such as that a machine well constructed may engage in self-replication, while universal construction itself was simply assumed over a most minimal case. Universal construction under this standard is trivial. Hence, while all the configurations given here can construct any passive configuration, none can construct the real-time crossing organ devised by Gorman.<ref name="Automata2008"/>

[[Category:待整理页面]]

[[Category:待整理页面]]