A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert in 1928.
Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939. == Etymology == The word 'algorithm' has its roots in Latinizing the nisba, indicating his geographic origin, of the name of Persian mathematician Muhammad ibn Musa al-Khwarizmi to algorismus.
Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939. == Etymology == The word 'algorithm' has its roots in Latinizing the nisba, indicating his geographic origin, of the name of Persian mathematician Muhammad ibn Musa al-Khwarizmi to algorismus.
Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939. == Etymology == The word 'algorithm' has its roots in Latinizing the nisba, indicating his geographic origin, of the name of Persian mathematician Muhammad ibn Musa al-Khwarizmi to algorismus.
Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939. == Etymology == The word 'algorithm' has its roots in Latinizing the nisba, indicating his geographic origin, of the name of Persian mathematician Muhammad ibn Musa al-Khwarizmi to algorismus.
Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939. == Etymology == The word 'algorithm' has its roots in Latinizing the nisba, indicating his geographic origin, of the name of Persian mathematician Muhammad ibn Musa al-Khwarizmi to algorismus.
A notable failure due to exceptions is the Ariane 5 Flight 501 rocket failure (June 4, 1996). Proof of program correctness by use of mathematical induction: Knuth demonstrates the application of mathematical induction to an "extended" version of Euclid's algorithm, and he proposes "a general method applicable to proving the validity of any algorithm".
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