Fundamental issues of Computing Science
Http://bbs.xml.org.cn/dispbbs.asp? Boardid = 64 & id = 50970Scientific Problems refer to the subjects (persons) of scientific understanding in a certain era. On the basis of completed scientific knowledge and scientific practices, the problems that need to be solved and are likely to be solved. It includes a certain number of solutions and domains, but there is no definite answer. The history of scientific progress is a history in which scientific problems are constantly raised and solved. Not all questions about science can be called scientific questions. The main characteristics of scientific problems include: l the times, and any scientific problem has its characteristics of the times. L chaos and the proposal of scientific questions indicate that the existing knowledge is difficult to meet the needs of people to explore the world. People are eager for new knowledge, but it is ambiguous at the beginning. L resolvable: scientific problems must be solved. L variability: if a problem can lead to another scientific problem that can be solved, the original problem is still a scientific problem. L unsolved: scientific problems are unsolved. The fundamental problem of computing science is the most essential scientific problem in the field of computing, which plays a unified global role. What is
Fundamental issues of Computing ScienceIt is necessary to analyze the process of understanding the nature of "computing. [K1] a long time ago, ancient Chinese scholars believed that this problem can be solved only when a mathematical problem is determined that it can be solved by an abacus. This has already reflected the idea of algorithm, and has already included the fundamental problems that ancient Chinese scholars have on computing, that is
"Executable"A simple understanding of the problem. In the Middle Ages, philosophers raised a bold question: can we use machinery to implement individual functions of human brain activity [k2]? This directly led to the subsequent generation and manufacture of mechanical computing machines capable of simple mathematical operations. Including l 1641, French B. pascal made the first addition machine using gear technology; l German g in 1673. w. v. leibniz is based on Pascal to create a computing machine that can perform simple arithmetic operations. L in 1830s, C. Babbage, British, designed an analyzer used to calculate logarithm, triangle, and other arithmetic functions. L in 1920s, American v. Bush developed an electronic simulation computer capable of solving general differential equations. This computing history includes the exploration of the nature of the computing process and the fundamental problems of computing. However, yes
Formal methods and Theoretical ResearchComputing natureBreakthroughs have been made in recognition.The development of formal methods and theories
Originated from the basic research on Mathematics. The basic research of mathematics refers to the scientific research on the object, nature, general law of occurrence and development of mathematics. There are four important milestones. The first is the set theory proposed by German mathematician G. Cantor in 1874, which has become the basis of modern mathematics. The second is the Russell paradox proposed by B. Russel in 1901 Based on the set theory, which directly led to the third crisis in the history of mathematics development. The formal definition of the Russell paradox is S = {x | X does not belong to s }. In order to eliminate the Paradox and save the foundation of the mathematical building, the basic research of mathematics has gradually formed three schools: logical, intuition, and formalism. At the beginning of the 20th century, D. Hilbert, a representative of the formalism, proposed the famous "Hilbert program" and became the third landmark. The Hilbert Program proposes that every mathematical branch should be formally formed into a form system, and these formal branches should be used as objects to construct a mathematical metatheory to prove the compatibility of each form system, to export the compatibility of all mathematics. The essence of the Hilbert program is to find a general formal logic system, and the system should be complete. In this system, the authenticity of any given proposition can be determined mechanically. The basis of the Hilbert program is logic and algebra, derived from the Boolean algebra system created by the British mathematician G. Boole in the 19th century. Unfortunately, in 1931, the 25-year-old Austrian mathematician K. Godel proved the Incompleteness Theorem of the formal system and declared the failure of the Hilbert program. This is also the fourth landmark in mathematics basic research. Godel's Incompleteness Theorem points out that there is no perfect form system as Hilbert expects. Any form system is incomplete and cannot exhaust all mathematical propositions, any form system has a proposition that the system cannot determine its authenticity, that is, there is an unsolvable problem in any form system. Although the Hilbert program failed, it, together with the incomplete theorem of Godel, promoted people's understanding of the essence of computational science. For example, it inspires computer scientists to avoid spending their energy to prove problems that cannot be judged. Instead, they should focus on solving problems that are "executable. So far, the "Essence of computing" was finally revealed by Turing. In the late 1930s S, the mathematician Turing (. m. turning refers to the essence of computing through the Turing Machine of constructor. This essence is described in natural language as follows: Any computing can be restored to a computer (human or machine) in essence) transform a string of 0 and 1 on a tape that can be infinitely prolonged at both ends, and finally obtain a conversion process that meets the predefined symbol string. Turing's research result is a deepening of Godel's research results. The results show that there are some problems that cannot be solved by any mechanical process, that is, some problems are not solved by the Turing machine. Since any numeric value and non-Numeric (letters, symbols, etc.) objects can be encoded as strings, they can be interpreted as both data and
It is interpreted as an instruction. Therefore, any computing process can be encoded and stored in the memory.[K3] Turing's description of the essence of computation reveals the executive nature of computation and puts forward the concept of Computability. It is said that a problem is computable, and only when it is turing computable. However, a problem is that Turing is computable, and only when it has a graphic machine can solve the problem. The algorithm is an algorithm that can be executed by a Turing Machine and shut down. Any computation problem is ultimately attributed to the Turing computing problem, which is the famous Qiu Qi-Turing topic. With an understanding of the nature of computing, you can understand the research contents and fundamental problems of computing science. Computing Science is a scientific field that systematically studies the algorithm process for describing and transforming information. Its research covers algorithms, Computability, and implementation issues based on computing hardware and software. The fundamental question of computing science is: what can be effectively automated, that is, the enforceability of objects. All discussions related to enforceability are dealing with discrete objects. It is difficult for continuous objects to perform (Automated) Processing of [K4]. Therefore, the fundamental problem of Computing Science determines that the structure of the computer itself and the objects it processes are discrete. Continuous objects can be processed by computers only after they are discretization. To put it more directly, the fundamental task of all the branches of computing science is "computing ",
The essence is the string transformation.[K5] http://www.math.org.cn/forums/index.php? Showtopic = 18902 mathematics is the mother of science, and computer science is developed from discrete mathematics. CS mainly studies formal algorithms. Because the formal algorithm ensures that
Enforceability[K6]; constructive mathematics is its theoretical basis, because computer algorithms are structured [K7.
Computing Theory is an abstract description of the nature of computers. It is also the core content of Theoretical Computer Science. Not numerical combination algorithms are the soul of computers, but also the fundamental guarantee that computers can be widely used, (it makes the logical relationships of all things in the world a high degree of mathematical abstraction to form an algorithm class. The program is based on these algorithm classes [K8]), so it is the core content of computer science; comparatively speaking, the numerical calculation method is more important to CS, and it is more necessary for scientific computing.
[K1] fundamental question of computing science [k2] Bold question [K3] commands (that is, the operation process) can also be encoded !! [K4] Why is it difficult for continuous objects to be processed automatically ??? [K5]! The essence is String Conversion ?!! [K6] enforceability [K7] What is the meaning of structure? [K8]
