Ha matematika, pagihap, lingwistika, analgoritmo amo an surundan nga naghahatag hin solusyon ha usa ka problema nga agsob gamiton ha pagkalkula ngan pag proseso hin mga datos.
Boolos, George; Jeffrey, Richard (1999) [1974]. Computability and Logic (4th ed.). Cambridge University Press, London. ISBN 0-521-20402-X.: cf. Chapter 3Turing machines where they discuss "certain enumerable sets not effectively (mechanically) enumerable".
Campagnolo, M.L.,Moore, C., and Costa, J.F. (2000) An analog characterization of the subrecursive functions. InProc. of the 4th Conference on Real Numbers and Computers, Odense University, pp. 91–109
Church, Alonzo (1936a). "An Unsolvable Problem of Elementary Number Theory".The American Journal of Mathematics.58 (2): 345–363.doi:10.2307/2371045.JSTOR2371045. Reprinted inThe Undecidable, p. 89ff. The first expression of "Church's Thesis". See in particular page 100 (The Undecidable) where he defines the notion of "effective calculability" in terms of "an algorithm", and he uses the word "terminates", etc.
Church, Alonzo (1936b). "A Note on the Entscheidungsproblem".The Journal of Symbolic Logic.1 (1): 40–41.doi:10.2307/2269326.JSTOR2269326.Church, Alonzo (1936). "Correction to a Note on the Entscheidungsproblem".The Journal of Symbolic Logic.1 (3): 101–102.doi:10.2307/2269030.JSTOR2269030. Reprinted inThe Undecidable, p. 110ff. Church shows that the Entscheidungsproblem is unsolvable in about 3 pages of text and 3 pages of footnotes.
Daffa', Ali Abdullah al- (1977). The Muslim contribution to mathematics. London: Croom Helm. ISBN 0-85664-464-1.
Hertzke, Allen D.; McRorie, Chris (1998). "The Concept of Moral Ecology". In Lawler, Peter Augustine; McConkey, Dale. Community and Political Thought Today. Westort, CT: Praeger.
Kleene, Stephen C. (1936)."General Recursive Functions of Natural Numbers".Mathematische Annalen.112 (5): 727–742.doi:10.1007/BF01565439. Ginhipos tikang hanorihinal han 2014-09-03. Ginkuhà2015-01-30. Presented to the American Mathematical Society, September 1935. Reprinted inThe Undecidable, p. 237ff. Kleene's definition of "general recursion" (known now as mu-recursion) was used by Church in his 1935 paperAn Unsolvable Problem of Elementary Number Theory that proved the "decision problem" to be "undecidable" (i.e., a negative result).
Kleene, Stephen C. (1943). "Recursive Predicates and Quantifiers".American Mathematical Society Transactions.54 (1): 41–73.doi:10.2307/1990131.JSTOR1990131. Reprinted inThe Undecidable, p. 255ff. Kleene refined his definition of "general recursion" and proceeded in his chapter "12. Algorithmic theories" to posit "Thesis I" (p. 274); he would later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis"(Kleene 1952:317) (i.e., theChurch thesis).
Kleene, Stephen C. (1952). Introduction to Metamathematics (First ed.). North-Holland Publishing Company. ISBN 0-7204-2103-9. 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 ed.). Prentice-Hall, Englewood Cliffs, NJ. ISBN 0-13-165449-7. Minsky expands his "...idea of an algorithm—an effective procedure..." in chapter 5.1Computability, Effective Procedures and Algorithms. Infinite machines.
Post, Emil (1936). "Finite Combinatory Processes, Formulation I".The Journal of Symbolic Logic.1 (3): 103–105.doi:10.2307/2269031.JSTOR2269031. Reprinted inThe 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-calledChurch–Turing thesis.
Rogers, Jr, Hartley (1987). Theory of Recursive Functions and Effective Computability. The MIT Press. ISBN 0-262-68052-1.
Rosser, J.B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem".Journal of Symbolic Logic.4. Reprinted inThe 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. (1972). Introduction to Computer Organization and Data Structures (1972 ed.). McGraw-Hill, New York. ISBN 0-07-061726-0. 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 analgorithm" (p. 4).
Turing, Alan M. (1936–37). "On Computable Numbers, With An Application to the Entscheidungsproblem".Proceedings of the London Mathematical Society, Series 2.42: 230–265.doi:10.1112/plms/s2-42.1.230.. Corrections, ibid, vol. 43(1937) pp. 544–546. Reprinted inThe Undecidable, p. 116ff. Turing's famous paper completed as a Master's dissertation while at King's College Cambridge UK.
Turing, Alan M. (1939). "Systems of Logic Based on Ordinals".Proceedings of the London Mathematical Society.45: 161–228.doi:10.1112/plms/s2-45.1.161. Reprinted inThe Undecidable, p. 155ff. Turing's paper that defined "the oracle" was his PhD thesis while at Princeton USA.
Wallach, Wendell; Allen, Colin (November 2008). Moral Machines: Teaching Robots Right from Wrong. USA: Oxford University Press. ISBN 978-0-19-537404-9.
Berlinski, David (2001). The Advent of the Algorithm: The 300-Year Journey from an Idea to the Computer. Harvest Books. ISBN 978-0-15-601391-8.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein (2009). Introduction To Algorithms, Third Edition. MIT Press. ISBN 978-0262033848.
