Symmetric $\Rightarrow$ All Outputs Equally Likely

• Instruction set symmetric $\Rightarrow M$ symmetric
• Both its rows and its columns will each sum to 1.0
• M is doubly stochastic
• Therefore in the limit all states are equally probable [Feller, 1970, page 399]

• If the instruction set is asymmetric $M_{ij} \neq M_{ji}$, there is still a limit but the states are no longer equally likely