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11 An Improved Algorithm to Accelerate Regular Expression Evaluation Authors: Michela Becchi and...
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11
An Improved Algorithm to Accelerate
Regular Expression Evaluation
Authors: Michela Becchi and Patrick Crowley
Publisher: ANCS’07Present: Kia-Tso Chang
Date: January 8 2008
7
Lemma
we define its depth as the minimum number of states visited when moving from s0 to s in the DFA.
Lemma: If none of the default transitions in a D2FA lead from a state with depth di to a state of depth dj with dj ≥ di, then any string of length N will require at most 2N state traversals to be processed.
10
Reducing the alphabet
Two symbols ci and cj will fall into the same class if they are treated the same way in all DFA states. In other words, given the transition function δ(states, Σ)→states,δ(s,ci)= δ(s,cj) for each state s belonging to the DFA