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La máquina de Turing No vamos a hablar de ALAN TURING Un poco de Historia Un poco de Historia 1812 Charles Babbage – Máquina diferencial Máquina calculadora de tablas matemáticas. La diseñó pero la construyó parcialmente. Cálculo de Funciones Polinómicas que aproximan a senos, cosenos, logaritmos, etc.. Un poco de Historia 1816-1871 Charles Babbage – Máquina Analítica Máquina analítica de propósito general. Sólo diseñó. Réplica en un museo de Londres Era programable con tarjetas perforadas. Lenguaje parecido a ensamblador. Ada Lovelace programadora. Un poco de Historia 1889 Herman Hollerith – Máquina Tabuladora Automatizó el censo americano Hollerith (ingeniero de minas) – Tabulating Machine Company 1890 - Tiempo de procesamiento humano 10 años, lo redujo a 6 semanas! Un poco de Historia 1936 Máquina de Turing Máquina universal abstracta http://www.aturingmachine.com/ Teoría de la computación que llevaría a la construcción del ordenador. Un poco de Historia 1939 Alan Turing - Bombe Dispositivo electro-mecánico. Descifrar códigos nazis de Enigma. 1920 – Enigma 1932 – Hitler gana elecciones & Marian Rejewski descifra códigos 1938 – Marian Rejewski diseña ‘Bombe’ 1939 – Alan Turing, Gordon Welchman y Harold Keen construyen ‘Bombe’ Parlamento Polaco a raiz de “The Imitation Game”: Controversia. La Máquina de Turing La máquina de Turing ¿Qué es un Número Computable? 1936 - Turing Un número computable es aquel para el que hay una máquina de Turing que dado un input termina con el n-ésimo dígito de ese número. Cálculo del número p Algoritmo de Chudnovsky ¿Qué es un Problema de decisión? ¿Es el 11 un número primo? ¿Es ababa un palíndromo? ¿Tardaré un tiempo finito en hacer un cálculo? 1936 - Church-Turing Demostraron que NO existe algoritmo general capaz de decidir si una fórmula es un TEOREMA. Problema de decisión = Problema de la parada 1936 - Turing Dada una máquina de Turing y un input, en general es imposible saber si la Máquina se parará. La máquina de Turing • Cinta con cuadrados. • Cada cuadrado es capaz de almacenar un símbolo del conjunto . • S es el input que pertenece al conjunto . • La máquina empieza que el input S . • Estado Inicial es q0 • En cada paso la máquina está en un estado q, lee un símbolo s, escribe un nuevo símbolo, cambia de estado y se mueve a la izquierda o derecha. q 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 La máquina de Turing • Formalmente una MAQUINA DE TURING es: función de transición input estados alfabeto q 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 Ejemplo Ejemplo de Código x 2x + 1 Números binarios x 2x + 1 Multiplicar por 2 un binario 3 x 2 = 6 4 x 2 = 8 Sumar 1 a un binario 3 + 1 = 4 6 + 1 = 7 Acabando… • 1931 – Gödel: “Toda teoría axiomática contiene proposiciones indecidibles: siempre habrá en ella afirmaciones verdaderas que no pueden demostrarse. • 1936 – Turing: Inicio oficial de la informática. Padre de la teoría de la computabilidad. • Aplicación en la Teoría de la complejidad. • La existencia de La máquina de Turing es en esencia la existencia de los algoritmos (ordenadores actuales) Gracias por vuestra atención .

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Timeline of Computer History
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