Abstract
In this paper, a family of automata for weak factor recognition named weak factor automaton (WFA) is introduced. WFAs can at least recognize the factors of a word and have similar properties of the factor oracle. WFAs are not always acyclic and the acyclic WFA is equivalent to the factor oracle with redundant edges. Based on the same approach, a new weight automaton for precise full-text index is introduced. A simple linear on-line construction algorithm for these two classes of automata is also given.
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