A speed-up of oblivious multi-head finite automata by cellular automata

International audienceIn this paper, we present a parallel speed-up of a simple, yet significantly powerful, sequential model by cellular automata. The simulated model is called oblivious multi-head finite automata and is characterized by the fact that the trajectory of the heads only depends on the length of the input word. While the original $k$-head finite automaton works in time O(\cramped{n^k}), its corresponding cellular automaton performs the same task in time O(\cramped{n^{k - 1}}\log(n)) and space O(\cramped{n^{k - 1}})