--- 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