... that ,we set . For all such that and , we set . For all such that and , we create a new intermediatebackoff state and set ; then for all , if, we add a transitionto .Proposition 3 The WFA ... length of is . Hence, the cost of finding all for a given is . Therefore, the total cost is . For all non-empty , we create a new state and for all we set . We create a transition, and for all such ... construction of for allis , where is the n-gram order.Proof. For each and each , there are atmost possible states such that for some , and . It is trivial to see from the proof of lemma 2 that the maximum...