On the size of Boyer–Moore automata

In this work we study the size of Boyer–Moore automata introduced in Knuth, Morris & Pratt’s famous paper on pattern matching. We experimentally show that a finite class of binary patterns produce very large Boyer–Moore automata, and find one particular case which we conjecture, generates automata of size Ω ( m 6 ) . Further experimental results suggest that the maximal size could be a polynomial of O ( m 7 ) , or even an exponential O ( 2 0.4 m ) , where m is the length of the pattern.