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

Alex Borelllo, Gaetan Richard & Veronique Terrier
In 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 $O(n^k)$, its corresponding cellular automaton performs the same task in time $O(n^(k-1)log(n))$ and space $O(n^(k - 1))$.
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