# Theorem: Input/Output Equivalence

Simulation between two machines indicates that one abstracts the other. Bisimulation indicates that they have equivalent input/output behavior. These results rest on the following theorem and corollary:

**Theorem.** Let *B* simulate *A*.Then

*Behaviors** _{A}*
⊂

*Behaviors*.

_{B}Intuitively, the theorem simply states that *B* can match every move of
*A* and produce the same output sequence. It also implies that if *B*
cannot produce a particular output sequence, then neither can *A*. This
is stated formally in the following corollary.

**Corollary. **Let *B* simulate *A*.Then if (*x*, *y*)
∉
*Behaviors_{B}*
then (

*x,*

*y*) ∉

*Behaviors*

*.*

_{A}