In this paper, we present the simulation of a simple, yet significantly
powerful, sequential model by cellular automata. The simulated model is called
oblivious multi-head one-way finite automata and is characterized by having its
heads moving only forward, on a trajectory that only depends on the length of
the input. While the original finite automaton works in linear time, its
corresponding cellular automaton performs the same task in real time, that is,
exactly the length of the input. Although not truly a speed-up, the simulation
may be interesting and reminds us of the open question about the equivalence of
linear and real times on cellular automata.Comment: Journ\'ees Automates Cellulaires 2010, Turku : Finland (2010