The nature of computation : logic algorithms applications : 9th Conference on Computability in Europe CiE 2013 Milan Italy July 1 5 2013 ; proceedings This book constitutes the refereed proceedings of the 9th Conference on Computability in Europe CiE 2013 held in Milan Italy in July 2013. The 48 revised papers presented together with 1 invited lecture and 2 tutorials were carefully reviewed and selected with an acceptance rate of under 31 7%. Both the conference series and the association promote the development of computability related science ranging over mathematics computer science and applications in various natural and engineering sciences such as physics and biology and also including the promotion of related non scientific fields such as philosophy and history of computing.