Running time complexity of printing an acyclic automaton

Authors:
Franck Guingne;André Kempe;Florent Nicart
Affiliations:
Xerox Research Centre Europe, Grenoble Laboratory, Meylan, France and Laboratoire d'Informatique Fondamentale et Appliquée de Rouen, Faculté des Sciences et des Techniques, Universit ...;Xerox Research Centre Europe, Grenoble Laboratory, Meylan, France;Xerox Research Centre Europe, Grenoble Laboratory, Meylan, France and Laboratoire d'Informatique Fondamentale et Appliquée de Rouen, Faculté des Sciences et des Techniques, Universit ...
Venue:
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Year:
2003

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Abstract

This article estimates the worst-case running time complexity for traversing and printing all successful paths of a normalized trim acyclic automaton. First, we show that the worst-case structure is a festoon with distribution of arcs on states as uniform as possible. Then, we prove that the complexity is maximum when we have a distribution of e (Napier constant) outgoing arcs per state on average, and that it can be exponential in the number of arcs.