- transitions do not increase the power of an NFA . That is, any - NFA ( NFA with transition), we can always construct an equivalent NFA without -transitions. The equivalent NFA must keep track where the NFA goes at every step during computation. This can be done by adding extra transitions for removal of every - transitions from the - NFA as follows.

If we removed the - transition from the - NFA , then we need to moves from state p to all the state on input symbol which are reachable from state q (in the - NFA ) on same input symbol q. This will allow the modified NFA to move from state p to all states on some input symbols which were possible in case of -NFA on the same input symbol. This process is stated formally in the following theories.

Theorem if L is accepted by an - NFA N , then there is some equivalent without transitions accepting the same language L

Proof:

          Let be the given with

We construct