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Semenov / Uspensky

Algorithms: Main Ideas and Applications

Medium: Buch
ISBN: 978-0-7923-2210-8
Verlag: Springer Netherlands
Erscheinungstermin: 31.03.1993
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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]).

Produkteigenschaften

  • Artikelnummer: 9780792322108
  • Medium: Buch
  • ISBN: 978-0-7923-2210-8
  • Verlag: Springer Netherlands
  • Erscheinungstermin: 31.03.1993
  • Sprache(n): Englisch
  • Auflage: 1993
  • Serie: Mathematics and Its Applications
  • Produktform: Gebunden
  • Gewicht: 1290 g
  • Seiten: 270
  • Format (B x H x T): 160 x 241 x 20 mm
  • Ausgabetyp: Kein, Unbekannt

Themen

Autoren/Hrsg.

Autoren

Notation and Terminology.- 1.0 Preliminary notions of the theory of algorithms: constructive objects and aggregates; local properties and local actions.- 1.1 The general notion of an algorithm as an independent (separate) concept.- 1.2 Representative computational models.- 1.3 The general notion of a calculus as an independent (separate) concept.- 1.4 Representative generating models.- 1.5 Interrelations between algorithms and calculuses.- 1.6 Time and Space as complexities of computation and generation.- 1.7 Computable functions and generable sets; decidable sets; enumerable sets.- 1.8 The concept of a ?-recursive function.- 1.9 Possibility of an arithmetical and even Diophantine representation of any enumerable set of natural numbers.- 1.10 Construction of an undecidable generable set.- 1.11 Post’s reducibility problem.- 1.12 The concept of a relative algorithm, or an oracle algorithm.- 1.13 The concept of a computable operation.- 1.14 The concept of a program; programs as objects of computation and generation.- 1.15 The concept of a numbering and the theory of numberings.- 1.16 First steps in the invariant, or machine-independent, theory of complexity of computations.- 1.17 The theory of complexity and entropy of constructive objects.- 1.18 Convenient computational models.- 2.1 Investigations of mass problems.- 2.2 Applications to the foundations of mathematics: constructive semantics.- 2.3 Applications to mathematical logic: formalized languages of logic and arithmetic.- 2.4 Computable analysis.- 2.5 Numbered structures.- 2.6 Applications to probability theory: definitions of a random sequence.- 2.7 Applications to information theory: the algorithmic approach to the concept of quantity of information.- 2.8 Complexity bounds for particular problems.- 2.9 Influenceof the theory of algorithms on algorithmic practice.- Appendix. Probabilistic Algorithms (How the Use of Randomness Makes Computations Shorter).- A.1 Preliminary remarks.- A.2 Main results.- A.3 Formal definitions.- References.- Author Index.