Fast language acceptance by shrinking cellular automata

Abstract When bounded cellular automata are used as acceptors for formal languages, the number of time steps required to accept a string σ is at least ¦σ¦, except in certain trivial cases, since the distinguished cell's state after t steps cannot depend on the initial states of the cells at distances > t from it. However, if the automaton is allowed to shrink (i.e., cells are deleted, and their predecessors become directly connected to their successors), language acceptance in less than linear time becomes possible.