Compressed automata for dictionary matching

We address a variant of the dictionary matching problem where the dictionary is represented by a straight line program (SLP). For a given SLP-compressed dictionary D of size n and height h representing m patterns of total length N, we present an O ( n 2 log ? N ) -size representation of Aho-Corasick automaton which recognizes all occurrences of the patterns in D in amortized O ( h + m ) running time per character. We also propose an algorithm to construct this compressed Aho-Corasick automaton in O ( n 3 log ? n log ? N ) time and O ( n 2 log ? N ) space. In a spacial case where D represents only a single pattern, we present an O ( n log ? N ) -size representation of the Morris-Pratt automaton which permits us to find all occurrences of the pattern in amortized O ( h ) running time per character, and we show how to construct this representation in O ( n 3 log ? n log ? N ) time with O ( n 2 log ? N ) working space.

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