摇尾乞怜 发表于 2025-3-21 19:17:51
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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 cinstate 发表于 2025-3-22 04:08:31
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 , , ). Mathematical roots of the concept of a calculus go back to antiquity (see ). Games with strict rules — such as chess, dominoes, majong — are prEpithelium 发表于 2025-3-22 06:13:46
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 oGerminate 发表于 2025-3-22 08:44:52
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 functinterlude 发表于 2025-3-22 16:31:42
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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