Arbor, Vol 189, No 764 (2013)

Alan Turing y los orígenes de la complejidad


https://doi.org/10.3989/arbor.2013.764n6006

Miguel Angel Martin-Delgado
Departamento de Física Teórica I, Universidad Complutense, España

Resumen


El 75 aniversario del artículo seminal de Turing y el centenario de su nacimiento ocurren en 2011 y 2012, respectivamente. Es natural revisar y valorar las contribuciones que hizo Turing en campos muy diversos a la luz de los desarrollos que sus pensamientos han producido en muchas comunidades científicas. Aquí, la idea principal es discutir como el trabajo de Turing nos permite cambiar nuestra visión sobre los fundamentos de las Matemáticas, de forma similar a como la mecánica cuántica cambió nuestra concepción de la Física. Nociones básicas como compatibilidad y universalidad se discuten en un contexto amplio, haciendo énfasis especial en como a la noción de complejidad se le puede dar un significado preciso después de Turing, es decir, no solo cualitativo sino cuantitativo. Al trabajo de Turing se le da una perspectiva histórica en relación a algunos de sus precursores, contemporáneos y matemáticos que tomaron y llevaron sus ideas aún más allá.

Palabras clave


Máquina de Turing; Computabilidad; Complejidad Algorítmica; Complejidad Computacional; Clases de Complejidad; Omega de Chaitin; Entropía Algorítmica; Barrera de Turing

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