# Not Theorem!

Note that the theorem **does not **say that if

*Behaviors** _{A}*
⊂

*Behaviors*

_{B}then *B* simulates *A*. In fact, that assertion is false! Consider
the following two machines:

These two machines have exactly the same behaviors. Thus, it is certainly true
that *Behaviors** _{A}*
⊂

*Behaviors*(recall that ⊂ means "subset or equal" in our notation). However, (b) does not simulate (a). To see this, note that there is no state in (b) that you can pair with

_{B}*b*and still be able to match any move that machine (a) takes.