On the bit-parallel simulation of the nondeterministic Aho–Corasick and suffix automata for a set of patterns

In this paper we present a method to simulate, using the bit-parallelism technique, the nondeterministic Aho–Corasick automaton and the nondeterministic suffix automaton induced by the trie and by the Directed Acyclic Word Graph for a set of patterns, respectively. When the prefix redundancy is nonnegligible, this method yields—if compared to the original bit-parallel encoding with no prefix factorization—a representation that requires smaller bit-vectors and, correspondingly, less words. In particular, if we restrict to single-word bit-vectors, more patterns can be packed into a word.We also present two simple algorithms, based on such a technique, for searching a set PP of patterns in a text T of length n over an alphabet Σ of size σ. Our algorithms, named Log-And and Backward-Log-And, require O((m+σ)⌈m/w⌉)O((m+σ)⌈m/w⌉)-space, and work in O(n⌈m/w⌉)O(n⌈m/w⌉) and O(n⌈m/w⌉lmin)O(n⌈m/w⌉lmin) worst-case searching time, respectively, where w is the number of bits in a computer word, m   is the number of states of the automaton, and lminlmin is the length of the shortest pattern in PP.