物理系统中的计算
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模板:Original research 模板:Refimprove Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm).[1][2]
Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm).Computation from the Free Merriam-Webster Dictionary
计算是任何类型的算术或非算术计算，遵循一个良好定义的模型(例如，一个算法)。《韦氏词典》中的计算
Mechanical or electronic devices (or, historically, people) that perform computations are known as computers. An especially well-known discipline of the study of computation is computer science.
Mechanical or electronic devices (or, historically, people) that perform computations are known as computers. An especially well-known discipline of the study of computation is computer science.
执行计算的机械或电子设备(或者，从历史上看，人)被称为计算机。计算机科学是计算机科学研究中一个特别著名的学科。
Physical process
Computation can be seen as a purely physical process occurring inside a closed physical system called a computer. Examples of such physical systems are digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers, and wetware computers.
Computation can be seen as a purely physical process occurring inside a closed physical system called a computer. Examples of such physical systems are digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers, and wetware computers.
物理过程可以看作是一个纯粹的物理过程，发生在一个叫做计算机的封闭的物理系统中。这类物理系统的例子有数字计算机、机械计算机、量子计算机、 DNA 计算机、分子计算机、基于微流体的计算机、模拟计算机和人工智能计算机。
This point of view has been adopted by the physics of computation, a branch of theoretical physics, as well as the field of natural computing.
This point of view has been adopted by the physics of computation, a branch of theoretical physics, as well as the field of natural computing.
这种观点已经被理论物理学的一个分支计算物理所采纳，同时也被自然计算领域所采纳。
An even more radical point of view, pancomputationalism, is the postulate of digital physics that argues that the evolution of the universe is itself a computation.
An even more radical point of view, pancomputationalism, is the postulate of digital physics that argues that the evolution of the universe is itself a computation.
一个更激进的观点，泛计算主义，是数字物理学的假设，认为宇宙的演化本身就是一种计算。
The mapping account
The classic account of computation is found throughout the works of Hilary Putnam and others. Peter Godfrey-Smith has dubbed this the "simple mapping account."[3] Gualtiero Piccinini's summary of this account states that a physical system can be said to perform a specific computation when there is a mapping between the state of that system and the computation such that the "microphysical states [of the system] mirror the state transitions between the computational states."[4]
The classic account of computation is found throughout the works of Hilary Putnam and others. Peter Godfrey-Smith has dubbed this the "simple mapping account." Gualtiero Piccinini's summary of this account states that a physical system can be said to perform a specific computation when there is a mapping between the state of that system and the computation such that the "microphysical states [of the system] mirror the state transitions between the computational states."
在 Hilary Putnam 和其他人的著作中都可以找到计算的经典描述。彼得•戈弗雷-史密斯(petergodfrey-smith)将此称为“简单的映射账户”Gualtiero Piccinini 对这一说法的总结指出，当一个物理系统的状态与计算之间存在映射时，可以说该物理系统执行了一个特定的计算，这种映射是“(该系统的)微物理状态反映了计算状态之间的状态转换”
The semantic account
Philosophers such as Jerry Fodor[5] have suggested various accounts of computation with the restriction that semantic content be a necessary condition for computation (that is, what differentiates an arbitrary physical system from a computing system is that the operands of the computation represent something). This notion attempts to prevent the logical abstraction of the mapping account of pancomputationalism, the idea that everything can be said to be computing everything.
Philosophers such as Jerry Fodor have suggested various accounts of computation with the restriction that semantic content be a necessary condition for computation (that is, what differentiates an arbitrary physical system from a computing system is that the operands of the computation represent something). This notion attempts to prevent the logical abstraction of the mapping account of pancomputationalism, the idea that everything can be said to be computing everything.
= = = 语义解释 = = 哲学家，如 Jerry Fodor，提出了各种计算的解释，限制语义内容是计算的必要条件(也就是说，任意物理系统与计算系统的区别在于计算的操作数代表了某种东西)。这个概念试图阻止泛计算主义的映射帐户的逻辑抽象，泛计算主义认为一切都可以说是计算一切。
The mechanistic account
Gualtiero Piccinini proposes an account of computation based on mechanical philosophy. It states that physical computing systems are types of mechanisms that, by design, perform physical computation, or the manipulation (by a functional mechanism) of a "medium-independent" vehicle according to a rule. "Medium-independence" requires that the property can be instantiated模板:Clarify by multiple realizers模板:Clarify and multiple mechanisms, and that the inputs and outputs of the mechanism also be multiply realizable. In short, medium-independence allows for the use of physical variables with properties other than voltage (as in typical digital computers); this is imperative in considering other types of computation, such as that which occurs in the brain or in a quantum computer. A rule, in this sense, provides a mapping among inputs, outputs, and internal states of the physical computing system.[6]
Gualtiero Piccinini proposes an account of computation based on mechanical philosophy. It states that physical computing systems are types of mechanisms that, by design, perform physical computation, or the manipulation (by a functional mechanism) of a "medium-independent" vehicle according to a rule. "Medium-independence" requires that the property can be instantiated by multiple realizers and multiple mechanisms, and that the inputs and outputs of the mechanism also be multiply realizable. In short, medium-independence allows for the use of physical variables with properties other than voltage (as in typical digital computers); this is imperative in considering other types of computation, such as that which occurs in the brain or in a quantum computer. A rule, in this sense, provides a mapping among inputs, outputs, and internal states of the physical computing system.
机械论的解释基于机械哲学提出了计算的解释。它指出，物理计算系统是机制的类型，按照设计，执行物理计算，或操纵(通过一个功能机制)的“中等独立”的车辆根据规则。“中等独立性”要求属性可以由多个重新实现器和多个机制实例化，并且该机制的输入和输出也可以多重实现。简而言之，介质独立允许使用具有电压以外属性的物理变量(如典型的数字计算机) ; 这在考虑其他类型的计算时是必要的，如在大脑或量子计算机中发生的计算。在这个意义上，规则提供了物理计算系统的输入、输出和内部状态之间的映射。
Mathematical models
In the theory of computation, a diversity of mathematical models of computers has been developed. Typical mathematical models of computers are the following:
- State models including Turing machine, pushdown automaton, finite state automaton, and PRAM
- Functional models including lambda calculus
- Logical models including logic programming
- Concurrent models including actor model and process calculi
Giunti calls the models studied by computation theory computational systems, and he argues that all of them are mathematical dynamical systems with discrete time and discrete state space.[7]:ch.1 He maintains that a computational system is a complex object which consists of three parts. First, a mathematical dynamical system [math]\displaystyle{ DS }[/math] with discrete time and discrete state space; second, a computational setup [math]\displaystyle{ H=\left(F, B_F\right) }[/math], which is made up of a theoretical part [math]\displaystyle{ F }[/math], and a real part [math]\displaystyle{ B_F }[/math]; third, an interpretation [math]\displaystyle{ I_{DS,H} }[/math], which links the dynamical system [math]\displaystyle{ DS }[/math] with the setup [math]\displaystyle{ H }[/math].[8]:pp.179–80
In the theory of computation, a diversity of mathematical models of computers has been developed.
Typical mathematical models of computers are the following:
- State models including Turing machine, pushdown automaton, finite state automaton, and PRAM
- Functional models including lambda calculus
- Logical models including logic programming
- Concurrent models including actor model and process calculi
Giunti calls the models studied by computation theory computational systems, and he argues that all of them are mathematical dynamical systems with discrete time and discrete state space. He maintains that a computational system is a complex object which consists of three parts. First, a mathematical dynamical system DS with discrete time and discrete state space; second, a computational setup H=\left(F, B_F\right), which is made up of a theoretical part F, and a real part B_F; third, an interpretation I_{DS,H}, which links the dynamical system DS with the setup H.
= = 数学模型 = = 在美国，已经发展出多种多样的计算机数学模型计算理论。典型的计算机数学模型如下:
- 状态模型包括图灵机、下推自动机、有限状态自动机和 PRAM
- 函数模型包括 lambda 演算
- 逻辑模型包括逻辑编程
- 并行模型包括行动者模型和过程演算 Giunti 调用计算理论计算系统研究的模型，他认为所有这些都是离散时间和离散状态空间的数学动态系统。他认为计算系统是一个由三部分组成的复杂对象。首先，一个离散时间和离散状态空间的数学动力系统 DS; 其次，一个计算设置 h = left (f，b _ f right) ，它由一个理论部分 f 和一个实际部分 b _ f 组成; 第三，一个解释 i { DS，h } ，它把动力系统 DS 和设置 h 联系起来。
See also
- Computationalism
- Real computation
- Reversible computation
- Hypercomputation
- Lateral computing
- Computational problem
- Multiple realizability
- Limits of computation
- Computationalism
- Real computation
- Reversible computation
- Hypercomputation
- Lateral computing
- Computational problem
- Multiple realizability
- Limits of computation
= = =
- 计算主义
- 实际计算
- 可逆计算
- 超计算
- 横向计算
- 计算问题
- 多重实现
- 计算极限
References
- ↑ Computation from the Free Merriam-Webster Dictionary
- ↑ "Computation: Definition and Synonyms from Answers.com". Answers.com. Archived from the original on 22 February 2009. Retrieved 26 April 2017.
- ↑ Godfrey-Smith, P. (2009), "Triviality Arguments against Functionalism", Philosophical Studies, 145 (2): 273–95, doi:10.1007/s11098-008-9231-3
- ↑ Piccinini, Gualtiero (2015). Physical Computation: A Mechanistic Account. Oxford: Oxford University Press. p. 18. ISBN 9780199658855.
- ↑ Fodor, J. A. (1986), "The Mind-Body Problem", Scientific American, 244 (January 1986)
- ↑ Piccinini, Gualtiero (2015). Physical Computation: A Mechanistic Account. Oxford: Oxford University Press. p. 10. ISBN 9780199658855.
- ↑ Giunti, Marco (1997). Computation, Dynamics, and Cognition. New York: Oxford University Press. ISBN 978-0-19-509009-3.
- ↑ Giunti, Marco (2017), "What is a Physical Realization of a Computational System?", Isonomia -- Epistemologica, 9: 177–92, ISSN 2037-4348
Category:Theoretical computer science Category:Computability theory
类别: 理论计算机科学类别: 可计算性理论
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