# HG changeset patch # User Christian Urban # Date 1360212961 0 # Node ID 9b9e0d37fc19cba507da2584e044db09b579c7df # Parent a4601143db905df4bee48324ba345e28fb4fca02 updated paper diff -r a4601143db90 -r 9b9e0d37fc19 Paper/Paper.thy --- a/Paper/Paper.thy Thu Feb 07 04:53:29 2013 +0000 +++ b/Paper/Paper.thy Thu Feb 07 04:56:01 2013 +0000 @@ -1392,14 +1392,15 @@ %also to one-sided Turing machines, which is needed for example in order to %formalise the undecidability of Wang's tiling problem \cite{Robinson71}. - While formalising the chapter in \cite{Boolos87} about universal Turing machines, an - unexpected outcome is that we identified an inconsistency in - their use of a definition. It is unexpected since it is a classic textbook which has - undergone several editions. The main idea is that every Turing machine started with - a standard tape computes a - partial arithmetic function. The inconsitency is when they define - when this function should \emph{not} return a result. They write in Chapter - 3 \cite[Page 32]{Boolos87}: + While formalising the chapter in \cite{Boolos87} about universal + Turing machines, an unexpected outcome of our work is that we + identified an inconsistency in their use of a definition. This is + unexpected since \cite{Boolos87} is a classic textbook which has + undergone several editions (we used the fifth edition). The central + idea about Turing machines is that when started with standard tapes + they compute a partial arithmetic function. The inconsitency is + when they define when this function should \emph{not} return a + result. They write in Chapter 3 \cite[Page 32]{Boolos87}: \begin{quote}\it ``If the function that is to be computed assigns no value to the arguments that