There are many kinds of fully homomorphic encryption scheme by using boolean circuits. And the plaintext space $\mathcal{P} = \{ 0,1 \}$.
If there is a -bit FHE scheme, we can construct a FHE scheme which can encrypt all the messages. For a string $x \in \{ 0,1 \}^{*}$ and $x = x_{1} \Vert x_{2} \Vert \cdots \Vert x_{n}$, we can define $$\mathrm{Enc}_{pk} (x) = y = \mathrm{Enc}_{pk} (x_{1}) \Vert \mathrm{Enc}_{pk} (x_{2}) \Vert \cdots \Vert \mathrm{Enc}_{pk} (x_{n})$$ where $x_{i} \in \{ 0,1 \}$
However, if I want to define a FHE with $\mathcal{P} = \{ 0,1 \}^*$, there is a problem.
Naturally, $$\mathrm{Enc}_{pk}: \mathcal{P} \rightarrow \mathcal{C}$$ $$\mathrm{Dec}_{sk}: \mathcal{C} \rightarrow \mathcal{P} \text{ or } \{\, \bot \,\}$$ $$\mathrm{Eval}: \mathcal{B} \times \mathcal{C}^* \rightarrow \mathcal{C}$$ where $\mathcal{B}$ is the set of all the boolean circuits.
Given $C \in \mathcal{B}$ such that $C \colon \{ 0,1 \}^{n} \rightarrow \{ 0,1 \}^m$, if $c \leftarrow \mathrm{Eval} (C, c_{1}, c_{2}, \ldots, c_{l})$, we have $$|\mathrm{Dec}_{sk}\left( c_{1} \right)| + |\mathrm{Dec}_{sk}\left( c_{2} \right)| + \cdots + |\mathrm{Dec}_{sk}\left( c_{l} \right)| = n$$ and $$|\mathrm{Dec}_{sk}\left( c \right)| = m$$ But, how can we know the size of $|\mathrm{Dec}_{sk}\left( c_{i} \right)|$ when we ask the access to $\mathrm{Eval}(\cdot, \cdot)$?