From 699d2cf4fa0f9a0d1c82edf27e0cccfb88b03023 Mon Sep 17 00:00:00 2001
From: "nathan.lhote" <nathan.lhote@lis-lab.fr>
Date: Mon, 20 Feb 2023 22:11:29 +0100
Subject: [PATCH] m

---
 main.tex | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/main.tex b/main.tex
index 7970e99..e498658 100644
--- a/main.tex
+++ b/main.tex
@@ -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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