Turing proposed the Turing machine model not to give the design of the computer at the same time, its meaning I think there are the following: 1. It proves the general computing theory, affirms the possibility of computer implementation, and it gives the main architecture that the computer should have; 2. The Turing machine model introduces the concepts of reading and writing, algorithms and programming languages, which greatly breaks through the design concept of the past computer; 3, Turing machine model theory is the core theory of computing discipline, because the computer's ultimate computing power is the computing power of the universal Turing machine, many problems can be transformed into the simple model of Turing machine to consider. Giving such a high rating to the Turing machine is not an overestimation, because from its design and operation, we can see the deep thoughts contained therein. The Universal Turing machine is equivalent to showing us a process in which the program and its inputs can be saved to the storage area first, and the Turing machine runs step by step until the result is given, and the result is also stored on the storage tape. In addition, we can vaguely see the main components of modern computers (in fact, the main components of von Neumann's theory), memory (equivalent to storage tape), central processing unit (controller and its state, and its alphabet can only have 0 And 1 two symbols), IO system (equivalent to the pre-input of the storage tape); 4, "Turing machine" is just an illusion of "computer", completely without considering the hardware state, the focus of consideration is the logical structure. In his book, Turing further designed a model called the “Universal Turing Machine.†The Turing machine can simulate the working state of any other Turing machine that solves a particular mathematical problem. Turing even imagined storing data and programs on the tape. The "Universal Turing Machine" is actually the most primitive model of modern general-purpose computers. 1) Why is there a problem with the Turing machine? 2) Why is the powerful Turing opportunity not going to stop? 3) Why did Turing originally design the Turing machine? Although the Turing machine is simple in construction, it is powerful, and it can simulate all the computing behavior of modern computers. It is the ultimate machine for computing. However, even this ultimate machine has problems that make it powerless. This is the first question to answer: Why is the Turing machine undecidable? First, it is clear what is Turing recognizable and Turing decidable. The object of recognition of the Turing machine is the language. Turing can recognize that it is not a language that Turing can recognize. (In this way, Chinese may be unrecognizable to Turing~). In fact, this is only an abbreviation. The full name should be recognized by the Turing machine. Turing machine recognizable language and Turing machine decidable language. A Turing machine may enter three states after reading a string: accept, reject, cycle, and if the Turing machine enters a loop state, it will never stop. Now suppose that there is language A. If you can design a Turing machine M, for any string ω, if ω ∈ A, then M will enter the acceptance state after reading ω, then A is a Turing identifiable language. Note that this definition does not limit the case where ω does not belong to A, so M reads ω that does not belong to A, so it may be rejected or looped. Turing can determine that the language requirements are more stringent. It requires that a Turing machine M be designed for language A: If ω ∈ A, M enters the acceptance state; otherwise, it enters the rejection state. If a language is Turing decimable, it is always possible to design a Turing machine that can determine whether a string belongs to the language within a finite number of steps. If a Turing machine always stops for all inputs, it is called a decider. However, the first question indicates that there must be problems that all the determiners cannot determine. To prove this, you have to start with Georg Cantor. Cantor's greatest contribution may be the creation of modern set theory, which he believes that some different infinite sets have different sizes. In 1891, Cantor published a five-page paper that proved that the cardinality of the real set is larger than the natural set, and in this paper, the legendary diagonal method was proposed (the method is clever but simple, there are I won't go into details.) The undecidable problem of the Turing machine requires the diagonal method. The fact that the real number set is "greater than" the natural number set can be thought of as: "infinity & TImes; infinity" is larger than "infinite & TImes; limited". Each natural number is finite, the set is a first-order infinity, and the natural number set is a first-order infinity; in contrast, a real number is a first-order infinity, and a set is a first-order infinity, then the set of real numbers is a second-order infinity. This first-order second-order is just my personal statement. With regard to the size relationship between different sets, Cantor proposes a continuum hypothesis, that is, Hilbert's first problem, that there is no base number that is absolutely larger than the countable set and absolutely smaller than the real number. The collection of sets, but this has nothing to do with today's topic, no longer unfolding. 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Turing machine meaning