A vector algorithm is an algorithm that applies a bounded number of vector operations to an input vector, regardless of the length of the input. In this paper, we describe the links between the existence of vector algorithms and the cascade decompositions of counter-free automata. We show that any computation that can be carried out with a counter-free automaton can be recast as a vector algorithm. Moreover, we show that for a class of automata that is closely related to algorithms in biocomputing, the complexity of the resulting algorithms is linear in the number of transitions of the original automaton.
['Anne Bergeron', 'Sylvie Hamel']
Cascade decompositions are bit-vector algorithms