Tuling
Sun Hong'an
(Jiangning Normal University)
Tuling, a. M. Born on June 23, 1912, was born in London, England; June 7, 1954, died in Wilmslow, United Kingdom. Mathematics, Mathematical Logic, Computer Science.
Father J. M. In the early years, the Tuling is at the Department of History of the University of Oxford University, and later from politics, they were sent to India and serve as officials of the Ministry of Civil Affairs. Mother E of Tuling S. Stoney is born in a railway engineer family, and he studied at the University of Technology, Paris University. Tuling is their second.
The Father of Tuling worked in India, and the mother often returned to India, and the children often live in a friend. The map is a unique intuitive creation ability and hobbies to mathematics. In 1926, he was admitted to the famous Sherborne, which was well received by London. He exhibited great interest and keen math brain during the secondary school. At the end of 1927, the 15-year-old Tuling is only to help her mother understand A. Einstein's relativity, writing Einstein's content, showing that he has a mathematical level and scientific understanding of unfixed. His interest in natural science made him a classmate c from 1930 and 1931. The natural science prize established by Morcom 's parents, awarded award-winning work entitled "The Reaction of Sulphurous Salt Upon Halogenide in Acidsolution), subject to government Distribution of the assisted supervision. The interest of natural science has laid the foundation for some of his later research. His mathematics ability has got him to win the King Edward Liu Dynasty Mathematics Golden Shield Medal at Middle School.
In 1931, Tuling was admitted to the King College of Cambridge University, got math scholarships due to excellent performance. In Cambridge, his mathematical ability is fully developed. In 1935, his first mathematical papers "Equivalence on Leftand Right Almost Priodicity" is published on "J. Lond.math.SOC.). On the same year, he also wrote the article "On Thegaussian Error Unction). This paper made him a college student as a researcher of the King College, and won the famous Smith Mathematics Award in the next year, and became one of the famous graduates who were famous for the King College.
In May 1936, Tuling wrote his most important mathematical results of the most important mathematical results "On Cable Numbers," On Computable Numbers, with an application to the entScheidungsproblem, this article In 1937, he was published in the "PROC.LOUD.MATH.SOC.) No. 42 of" PROC.LOUD.MATH.SOC.) Immediately causing extensive attention. In the text, he analyzed the calculation process, which gives the "general" computer concept that can be calculated any "can be calculated sequence" - a sequence of 0 and 1, and use this concept to solve D. A well-known judgment problem proposed by Hil-lbert. In 1937, another article "Cable Calculated and λ-Definability" broaden A. "Church" proposed "Church", forming "Church-Tutal Ability", which has the strictization of computational theory, and has the formation and development of computer science. In September 1936, Tuling was invited to study in the US Princeton Institute and work with Church. During the United States, he made some research on group theory and wrote a doctoral thesis. In 1938, he won his Ph.D. in Princeton. The topic of the paper is "Systems of Logic Based On Ordinal, 1939). Annual official published, a profound impact in the logic research.
In 1938, Tuling returned to the United Kingdom, still at the King University of Cambridge, continuing to study the logic and calculation theories in the Cambridge University, and started the development of computers. The Second World War interrupted his normal research work. In 1939, he should call to military work in the Communications Department of the British Foreign Ministry, mainly to solve the enemy's password. Due to the need for deciphering, he participated in the development of the earliest electronic computer in the world. His work has achieved excellent achievements, and thus won the highest prize of the government in 1945 - British Empire Honor Medal (O.B.E. Medal). It is believed that the concept of a general computer is a map spirit.
In 1945, Tuling ended the work of the Ministry of Foreign Affairs. He tried to recover the research in theory of theory in the theoretical computer science, and combined with the work of the war, develop a new computer. This idea is supported by the authorities. In the same year, Tuling was hired as researchers of Teddington National Physics Research Institute, which began the logic design and specific development of "Automatic Computer" (ACE). This year, Tuling wrote a design specification for the ACE (Proposals for Developmentin The Mathematlcs Divison of An Ace). This manual was officially published in 1972 after 27 years of confidentiality. Under the guidance of the design idea of Turing, the ACE prototype was made in 1950, and a large ACE machine was made in 1958.
In 1948, Tuling received senior lecturer in Manchester, and was designated as the assistant for the person in charge of the Manchester Automatic Digital Computer (MADAM) project, and concretely leading the mathematics of the project. As a summary of this work, 1950 Tuling prepared and published the "Manchester Electronic Computer Programmer Manual" (The Program Electronic Computer). During this period, he continued to conduct theoretical research in the logic logic. As early as 1947, Tuling proposed the idea of automatic programming. In 1950, he proposed the problem of machine thinking, his paper "ComputingMachiery and Intelligence, which has caused a wide care and far-reaching impact. In 1956, in the income of a collection of cultures, this article changed its "machine thinking? "(Cana Machine Think?) Is still one of the preferred readings of artificial intelligence.
In 1951, Tuling was elected as a member of the Royal Society. In 1952, he resigned from the position of the researcher of the King Cambridge University, concentrated on the University of Manchester. In addition to daily work and research work, he also guides some doctoral students, as well as a company that manufactures Manchester automatic digital computer - Fran-Ti's.
The interested interest in natural science has always made him happy to think about the natural science problem. At the end of the 1940s, he showed the strong interest in biology. In 1951, he wrote a constant article "The chemical basis of morphology" was published in the following year. He used mathematical tools to explain the biological form. And biochemical problems, the development of biomarics has been directly promoted.
Tulex is active, but personality is more inward. He is interested in sports. When you go to school in Cambridge, you will be able to take your hands in the 1940s. He has received 1 mile run and 3 miles of champions at the Games of the National Institute of Physics; I have received 3 miles of club champion; in 1947, he participated in the Marathon Championships held by British Amateur Federation and entered the top. 15, at this time, he has played four seas, and the newspaper called "Electronic Athlete". Tuling is unmarried. On June 7, 1954, Tuling may be due to accidental accidents - potassium cyanide poisoned in Wemslo himself.
Tuling is in science, especially in college logic and computer science, has achieved the world-famous achievements, and some of his scientific results constitute the foundation of modern computer technology.
1. Calcible theory
Calculation, it can be said that it is the most encountered mathematics topic, and in a long history of history, it has become an indispensable tool in people's social life. So what is calculation? Intuitively, the calculation generally refers to the process of converting a set of values to another (required) value using the rules specified in advance. For a certain type of problem, if you can find a set of determined rules, press this set of rules, and after given any of these questions, you can fully mechanically consider the results in a limited step, then say this Class issues can be calculated. This rule is an algorithm, which may also be called the problem of existing algorithms. This is the concept of intuitive energy calculating or algorithm.
Before the 20th century, it is widely believed that all the problems are algorithm, and people's calculation research is to find algorithms. It seems to prove all scientific propositions, at least all mathematical propositions exist algorithms, g. W. Leibniz has created the research work of mathematical logic. However, in the early 20th century, people found that there were many problems that have been long-term research, and they still can't find algorithms, such as Hilbert 10 questions, and the problem of half groups. So people have begun to suspect that whether these problems have not exist at all, that is, they are not calculated. This disseminability of course needs to be proven, when people discover, no matter whether the algorithm is still calculated, there is no precise definition! According to the aforementioned discussion of intuitive computable statements, there is no confirmation of the algorithm, because "completely mechanically" means? "Determined rules" refers to? Still not clear. In fact, there is no clear definition that cannot be abstainfully proved that there is an algorithm in which there is a problem, but the problem of the algorithm is generally confirmed by constructing an algorithm, so that the exact definition of the algorithm may not be involved. The need to solve the problem has prompted people to make an exploration. 1934, k. Godel in J. The concept of general recursive functions is proposed under the revelation of Herbrand, and it is pointed out that the algorithm can calculate functions are general recursive functions, and vice versa. 1936, c. Kleene is also avattern. Therefore, the algorithm can calculate the general recursive function of the function is then referred to as Elbown - Gödel-Kelin definition. In the same year, Church proves that his proposed λ-definition function is equivalent to the general recursive function, and proposes an algorithm to calculate functionality equivalent to general recursive functions or λ definition functions, which is a famous "clastological point".
Although the general recursive function gives a strict mathematical definition of the calculated function, in a specific calculation process, what is the initial function and the basic operations still have an uncertainty in a certain step. To eliminate all uncertainties, the Tulex defines the compute function from a new angle in his "Applicable Credits and Its Application in Judgment". He fully analyzes the calculation process of people, and the calculation is concluded as the simplest, most basic, and most determined operation action, thereby using a simple way to describe the intuitive mechanical basic calculation procedure, making any machine ( The program that can be destined can be around these actions. This simple method is based on an abstract automaton concept, and the result is: The algorithm can calculate the function is the function of this automatic machine. This not only gives a fully determined definition, but also linked the calculation and automaton for the first time, which has a huge impact on the later generation. This "automatic machine" was later called "Figure Ling".
The map spirit is a math model of an automaton. It is a paper strip of both ends (or one end). It is equipped with a square, and one letter in a certain alphabet is printed in each square. Space, recorded as S0); there is another read writing, which has a limited internal state. At any time, the writing head is watching a piece of checkered on the paper tape and performs the action specified by the conversion rule based on the content of the panel and the internal state of the read writing. Each Turing machine has a set of transform rules, which have one of the following three shapes:
Qiarqi, QIalqi, QIABQJ.
Mean: If the contents of the gaze are written when the writing head is in the status QI, the write head is first shifted, or the left is shifted, or the letter B is printed (ie change the content of the gaze. B.a, b can be S0). Tulex defines the calculated function as the map forever to calculate functions. In 1937, Tuling proved that the graphical calculated function and λ definition function is equivalent, thereby expanding the clastological point, resulting in: Algorithm ( Energy row) Calcible functions is equivalent to general recursive functions or λ definition functions or graphs and procedures can compute functions. This is the "Chuqi-Tutal Ability", which is quite perfect to solve the precise definition problem of the calculated function, which has entered a huge role in the development of the logic of mathematical logic.
The concept of the map spirit is very unique: if the interior state of the map spirit is interpreted as an instruction, the word in the alphabet is represented, and the input word input is also stored in the machine, which is an electronic computer. This created a discipline of "automatic machine" and promoted the development of electronic computers. At the same time, Tuling also proposes the concept of a general map spirit. It is equivalent to the general computer interpretation program, which directly promotes the design and development of the later general computer, and Tu Le himself also participated in this work. While giving a general japanese, the Tuling pointed out that the general map spirit is calculated, and its "mechanical complexity" is critical, exceeding this, and it is necessary to rely on the length and storage of the program. The amount is solved. This kind of thought opened the primary river that calculates complexity theory in computers.
2. Judgment problem
The so-called "determination problem" refers to whether the so-called "large number of problems" have algorithm solution, or whether there is a method of functionality such that each special case of the problem can mechanically determine whether it has a certain nature ( If it is true, whether it can be satisfied or have to have a problem, etc., as a result of a large number of problems itself).
The determination problem is closely related to the computable problem. The two can be defined in each other: If a certain type of problem can find the algorithm to determine if it has a certain nature, this type of problem is that this problem can be determined, or I can solve it; otherwise it is unrecoverable, or it is not understood. The two also distinguish: the problem is to determine if there is an algorithm that makes every special case for a class of problems to give a "yes" or "no" answer; calculated problem It is to find an algorithm to find some specific objects.
A great achievement on the problem is to determine the "shutdown problem" of the map spirit as a foundation of many judgment issues. Generally, a decision problem is attributed to a shutdown problem: "If the problem A can be determined, the stop problem can be determined "So" the "shutdown problem is" launch "problem A is unknovable."
The so-called shutdown refers to the interior of the charting machine reaches a result state, the status or symbol negative of the instruction table, resulting in calculation termination. At every moment, the state in which the machine is located, all lattices on the strip have been written on the strip of the symbol and the lattice location of the machine is currently known as the machine. The map spirit is starting from the initial pattern, and the initial pattern is transformed into the sequence of the pattern according to the step step. This process may continue without restrictions, or may encounter the state, symbol combination, or enter the end state in the instruction table. The pattern that is not asked to stop in the end condition is the final pattern, and this final pattern (if present) contains the calculation result of the machine. The so-called shutdown problem is: whether there is an algorithm that can determine whether any initial pattern can cause downtime? Tuling proves that such an algorithm does not exist, that is, the downtime is unknovable, so that it is a basis for solving many unknostable problems. In 1937, Tuling used his method to solve the famous Hilbert's judgment problem: the satisfaction of the narrow word calculation (also known as a first-order logic) formula. He encoded the graphline in the formula in the first-order logic, and then the unknropicity of the discrete to the problem of the problem of the charter shutdown. The "encoding method" created here has become one of the main methods of subsequent determinants of the formula class that proves the first-order logic.
On the judgment problem, the other results of the Tulex are the concept of map foreground proposed in 1939, and thereby export "Tu Legend" and relative recursive concepts. Using the concept of destinies and relative recursive, it can be compared to the degree of non-deterministic and non-recursive. On this basis, e. Perst (POST) put forward an important concept of unleaviveness, which has been significant in this regard.
Another famous judgment problem solved by Tuling is a "problem of half group", it is A. THUE (Thue) is proposed in 1914: whether there is an algorithm to determine if two any given words are equivalent [give limited different words called letters The symbol is given, and the alphabet is given, the finite sequence of the letter is called the word on the alphabet. The limited pair of words (A1, B1), ..., (AN, BN) are called a dictionary. If the two words R and S can change each other after using the limited dictionary, then these two words are equivalent]? 1947, Perster and A. A. Markov (Markov) is proved that this problem is unknovable. In 1950, Tuling further proved that the problem of satisfying a half group of elongate is also unknovable.
3. electronic calculator
The emergence and extensive application of electronic computers are one of the main signs of the new technology revolution in the 20th century. In a long period, people have always believed that the first electronic computer is American people press J. W. Mauchly proposed program in 1946, "Electronic Digital Integral and Automatic Computer" (ENIAC). The password decipherment work engaged in the Second World War involves the design and development of the electronic computer, but this work is strict. Until the 1970s, the intercom was disclosed. From some files, it is very likely that the world's first electronic computer is not ENIAC, but another machine related to Tuling, that is, Tulex's Co-Lossus developed in 1943 in 1943 (Giant The machine, the design of this machine uses some concepts proposed by Tulex. It used 1,500 tubes, using an optoelectronic reader; uses a perforated paper with input; and uses electronic pipe dual steady-state lines, performing counting, binary counts and Boolean logic operations, and the giant machine has produced 10 units, use them Deciphering the password is done well. In 1946, ENIAC was put into operation, shocked the world with its calculation speed (5000 computation per second). But before it is not completed, some people, including its main designers recognize that its control method is not applicable: ENIAC is not controlled by the program like the current computer, but uses hardware to use The logic circuit connected to the line plate and the conversion switch controls the operation. In this way, this machine can be used in a few minutes of finishing the complicated operation, but it is necessary to take a few hours or even ten hours to do it well. Therefore, how to automatically control operations to improve the key issues of improved electronic computer efficiency.
At the beginning of 1945, J. Von Neumann, Mochili et al. Proposed a famous Edvac [Electronic Discret Variable Automatic Comp-Uter, and proposes the overall idea of electronic computers controlled by the storage program. It is pointed out that such a computer should consist of five parts of the calculator, controller, memory, and input, output devices (later forming the so-called "Vonniman Way" of more than 40 years), but not proposed further Structural design. In 1945, the Bandh Tuling's Description of the ACE was first given, the structure of the storage program control computer was first given (the MADAM machine that Tuling later participated in the world was the largest electronic computer in the world). In this manual, the concept of the instruction register and instruction address register is first proposed, and the idea of subroutine and subscriptions is proposed, which is the most basic concept and ideas in modern electronic computing. Surprisingly, in this manual, Tuling has proposed the idea of "simulation system". The so-called simulation system means that the machine can not have a fixed instruction system, but it can simulate many functions of a computer with different instruction systems. . The ACE machine in the UK only uses the idea of Tuling, and for confidentiality, Tuling's ACE design instructions until 1972. During this time, people had to re-discovering things that Tuling had discovered, and in 1972, people have made a computer with simulation systems.
4. artificial intelligence
Tuling is one of the pioneers of artificial intelligence research. In fact, the map forever, especially the genericity model as a model of non-numerical symbols, contains a manual system that constructs certain intelligent behavior to achieve mental power. The idea of labor partial automation is the research objective of artificial intelligence. It is exactly from the concept of Tuli Machine. During the military work during the Second World War, Tuling often considers and discusses the "thinking machine" in our spare time, and carry out the "Machine Chess" Preliminary research work of class. In 1947, Tuling made a report entitled "Intelligent Machinery" on a computer, explained his thoughts on thinking machines, and pointed out from scientific perspectives: " The machine's activity is very similar to the machine that can be manufactured. "In the report, Tuling put forward the idea of automatic programming, namely the idea of constructing the program." Now automatic programming has become one of the basic topics of artificial intelligence. The ideas in the report of Tuling are extremely profound, novel, seem to be out of the imagination of people at the time. In 1959, this report was previously published for the first time, and it seems that people still have not attracted attention. Just in 1969, this report was once again published, and artificial intelligence has been quite progress, especially R. J. WaldingGer re-proposed the concept of automatic programming in 1969, and people began to understand the pioneering significance of this report.
In 1950, Tuling issued a famous "computer and intelligent" papers. This article gives a definition of behavioralism, and designs a famous "Tiantue Test", that is, a person in the case of non-contact objects (can be written by means of electricity If he cannot judge the object according to these question and answer, it is a person or a computer, so it can be considered that this computer has the same intelligence, Tuling is also proposed, and such a machine will appear at the end of the 20th century. This article of 1956 Tuling is re-published for "Can I think it is?" At this time, artificial intelligence has also entered the stage of practice. Tulex's machine intelligence thoughts are undoubtedly one of the direct origins of artificial intelligence. And with the in-depth research in the field of artificial intelligence, people are increasingly recognizing the deepness of Tulex's ideas: they are still one of the main ideas of artificial intelligence.
5. Other results
Tuling thought is active, and his creativity is also multi-faceted. According to colleagues, he has created several new statistical techniques in the secret work of the war, but did not form a paper published, and later re-established it to others, by A. Wald (Wald) was rediscovered and proposed "Sequential Analysis" is one of them. He also studied in group theory. In the article "Chemical Foundation of Morphology", he studied chemical substances that determine the color or morphology of the biological color (he called the formation) in the formation of a planar morphology (such as a cow. Spotting) and the distribution regulatory in the stereoscopic form (such as the distribution of radiophages and the leaflets), trying to explain the "physical chemistry laws can fully explain the facts of many form formation". In the biological industry, the topic began to discuss this issue in the 1980s. Tuling has also been subsequently referred to as "mathematical embryo". He also tried to study the construction of a human brain with a mathematical approach, such as estimating a problem of how many information that can store in the brain of a given number of neurons. These, so far, it is still a novel topic attracting many scientists.
