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Titlebook: Algorithms: Main Ideas and Applications; Vladimir Uspensky,Alexei Semenov Book 1993 Springer Science+Business Media B.V. 1993 Notation.alg

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发表于 2025-3-21 19:17:51 | 显示全部楼层 |阅读模式
期刊全称Algorithms: Main Ideas and Applications
影响因子2023Vladimir Uspensky,Alexei Semenov
视频video
学科分类Mathematics and Its Applications
图书封面Titlebook: Algorithms: Main Ideas and Applications;  Vladimir Uspensky,Alexei Semenov Book 1993 Springer Science+Business Media B.V. 1993 Notation.alg
影响因子Today the notion of the algorithm is familiar not only to mathematicians. It forms a conceptual base for information processing; the existence of a corresponding algorithm makes automatic information processing possible. The theory of algorithms (together with mathematical logic ) forms the the­ oretical basis for modern computer science (see [Sem Us 86]; this article is called "Mathematical Logic in Computer Science and Computing Practice" and in its title mathematical logic is understood in a broad sense including the theory of algorithms). However, not everyone realizes that the word "algorithm" includes a transformed toponym Khorezm. Algorithms were named after a great sci­ entist of medieval East, is al-Khwarizmi (where al-Khwarizmi means "from Khorezm"). He lived between c. 783 and 850 B.C. and the year 1983 was chosen to celebrate his 1200th birthday. A short biography of al-Khwarizmi compiled in the tenth century starts as follows: "al-Khwarizmi. His name is Muhammad ibn Musa, he is from Khoresm" (cited according to [Bul Rozen Ah 83, p.8]).
Pindex Book 1993
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发表于 2025-3-22 00:18:47 | 显示全部楼层
The general notion of an algorithm as an independent (separate) conceptemphasize that this discovery should not be confused with the discovery of representative computational models (constructed by Turing, Post, Markov, Kolmogorov); they will be discussed in chap. 1.2. Sometimes it is wrongly believed that the concept of an algorithm cannot be well understood without c
发表于 2025-3-22 04:08:31 | 显示全部楼层
The general notion of a calculus as an independent (separate) conceptinitions. The notion of a calculus reflects and generalizes an intuitive idea of inductive generation of a set (see [Mas 67], [Eb 70], [Mas 79]). Mathematical roots of the concept of a calculus go back to antiquity (see [Janovs 62]). Games with strict rules — such as chess, dominoes, majong — are pr
发表于 2025-3-22 06:13:46 | 显示全部楼层
Representative generating modelsany given calculus. (To be more exact we should speak not about representative but about .-representative models. Assume that . is an aggregate; a generating model is called . if for any calculus generating a subset of . there exists a calculus of this model generating the same subset.) The notion o
发表于 2025-3-22 08:44:52 | 显示全部楼层
Interrelations between algorithms and calculuseshe set of all pairs 〈., .〉 such that .(.) = .. On the other hand, (3) for any calculus there is an algorithm whose domain is a set generated by this calculus; and (4) any calculus generating a set of pairs 〈., .〉 being the graph of a function can be transformed into an algorithm computing this funct
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The concept of a computable operationive object from another, a computable operation effectively produces one set of constructive objects from another; informally, effectiveness here means that the operation makes it possible to generate the resulting set provided a process of generation of the argument is given. Because of the above s
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