Wikipedia طرفان
In mathematics and computing, an algorithm is a procedure (a finite [[set*Davis, Martin (2000). Engines of Logic: Mathematicians and the Origin of the Computer. New York: W. W. Nortion. Davis offers concise biographies of Leibniz, Boole, Frege, Cantor, Hilbert, Gödel and Turing with von Neumann as the show-stealing villain. Very brief bios of Joseph-Marie Jacquard, Babbage, Ada Lovelace, Claude Shannon, Howard Aiken, etc.
- سانچو:DADS
- Yuri Gurevich, Sequential Abstract State Machines Capture Sequential Algorithms, ACM Transactions on Computational Logic, Vol 1, no 1 (July 2000), pages 77-111. Includes bibliography of 33 sources.
- Kleene, Stephen C. (First Edition 1952). Introduction to Metamathematics, Tenth Edition 1991, North-Holland Publishing Company. Excellent -- accessible, readable -- reference source for mathematical "foundations".
- A. A. Markov (1954) Theory of algorithms. [Translated by Jacques J. Schorr-Kon and PST staff] Imprint Moscow, Academy of Sciences of the USSR, 1954 [i.e. Jerusalem, Israel Program for Scientific Translations, 1961; available from the Office of Technical Services, U.S. Dept. of Commerce, Washington] Description 444 p. 28 cm. Added t.p. in Russian Translation of Works of the Mathematical Institute, Academy of Sciences of the USSR, v. 42. Original title: Teoriya algerifmov. [QA248.M2943 Dartmouth College library. U.S. Dept. of Commerce, Office of Technical Services, number OTS 60-51085.]
- Minsky, Marvin (1967). Computation: Finite and Infinite Machines, First, Prentice-Hall, Englewood Cliffs, NJ. Minsky expands his "...idea of an algorithm -- an effective procedure..." in chapter 5.1 Computability, Effective Procedues and Algorithms. Infinite machines."
- Post, Emil (1936). "Finite Combinatory Processes, Formulation I". The Journal of Symbolic Logic 1: pp.103-105. Reprinted in The Undecidable, p. 289ff. Post defines a simple algorithmic-like process of a man writing marks or erasing marks and going from box to box and eventually halting, as he follows a list of simple instructions. This is cited by Kleene as one source of his "Thesis I", the so-called Church-Turing thesis.
- Rosser, J.B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". Journal of Symbolic Logic 4. Reprinted in The Undecidable, p. 223ff. Herein is Rosser's famous definition of "effective method": "...a method each step of which is precisely predetermined and which is certain to produce the answer in a finite number of steps... a machine which will then solve any problem of the set with no human intervention beyond inserting the question and (later) reading the answer" (p. 225-226, The Undecidable)
- Stone, Harold S.. Introduction to Computer Organization and Data Structures, 1972, McGraw-Hill, New York. Cf in particular the first chapter titled: Algorithms, Turing Machines, and Programs. His succinct informal definition: "...any sequence of instructions that can be obeyed by a robot, is called an algorithm" (p. 4).
- Hodges, Andrew. Alan Turing: The Enigma, (1983), Simon and Schuster, New York. , ISBN 0-671-49207-1. Cf Chapter "The Spirit of Truth" for a history leading to, and a discussion of, his proof.
