From cascade decompositions to bit-vector algorithms

Authors:
Anne Bergeron;Sylvie Hamel
Affiliations:
LACIM, Université du Québec à Montréal, C.P. 8888, Succursale Centre-Ville, Montréal, Québec, Canada, H3C 3P8;LACIM, Université du Québec à Montréal, C.P. 8888, Succursale Centre-Ville, Montréal, Québec, Canada, H3C 3P8
Venue:
Theoretical Computer Science - Implementation and application automata
Year:
2004

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Abstract

A vector algorithm is an algorithm that applies a bounded number of vector operations to an input vcctor, 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 bio-computing, the complexity of the resulting algorithms is linear in the number of transitions of the original automaton.