In circuit complexity we have one circuit for each input size. The size of the output is determined solely by the size of the input.So it seems to me that taken in its strict sense there are functions computable in $\mathsf{P}$ over $\{0,1\}^*$ which are not computable in $\mathsf{P/poly}$.This is partly caused by using $\{0,1,b\}$ in the Turing machine modelwhile in circuit model we only have $\{0,1\}$.Is there a nice standard way to deal with this issue that would work well for small complexity classes(e.g. it shouldn't change the complexity of computing AND of inputs too much,so encoding/decoding inputs/outputs is not a good solution)?Is there a simple modification of Turing machine model or circuit model which would make them correspond without this issue?
The size of output in circuit complexity
cc.complexity theory;circuit complexity;turing machines