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Commit 699d2cf4 authored by Nathan Lhote's avatar Nathan Lhote
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......@@ -35,6 +35,7 @@
\newcommand{\rtm}{\textsf{RTM}\xspace}
\newcommand{\drtm}{\textsf{DRTM}\xspace}
\newcommand{\reg}{\textsf{Reg}}
\newcommand{\homo}{\textsf{Hom}\xspace}
......@@ -74,7 +75,7 @@
\bibliographystyle{alpha}% the mandatory bibstyle
\title{\Expreg transductions} %TODO Please add
\title{\textsc{Exponential growth\\ word-to-word transductions}} %TODO Please add
\author{}
......@@ -359,13 +360,15 @@ For rational turing machines, the following hold:
\section{The case of the successor}
Let us denote by \homo the class of free monoid homomorphisms.
\begin{theorem}
\msomi with successor is equivalent to \dlinspace reductions.
$\homo \circ\msomi$ with successor is equivalent to \dlinspace reductions.
\end{theorem}
\begin{proof}
Given an \msomi, we can define a rational letter-to-letter relation which realizes the successor and from this obtain a linear bounded automaton.
From a linear bounded automaton, the next configuration relation can be defined in \mso.
From a linear bounded automaton, the next configuration relation can be defined in \mso. We use the homomorphism to erase the transitions that produce nothing.
\end{proof}
......
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