Allow us to say that our definition of a circuit is the one in every of a boolean circuit from [Vollmer].
He makes use of directed acyclic graphs to signify circuits the place the computation nodes are labeled with some features which come from a set of potential operations (referred to as foundation).

Allow us to say that we solely enable the operation $land$ for our circuit (i.e. the idea solely consists of $land$). Is $x land x$ a circuit if $x$ denotes an enter gate? I do not assume so, as a result of the enter gate $x$ is simply allowed to occure as soon as within the graph after which we would wish two edges to the $land$-node, i.e. we would wish a multigraph. A method round could be to pressure a foundation to have an identification operation. As an example utilizing the idea $land, id$ we might after all construct the $x land x$ circuit (that is additionally the case if we are able to construct the identification operation in some other method, e.g. if we’ve got $neg$ in our foundation) despite the fact that we’ve got to extend the dimensions of the circuit by utilizing $id$. It appears very counterintuitive that such a easy circuit is in truth not a circuit over the idea $land$, so is my reasoning right?

[Vollmer] Heribert Vollmer, Introduction to Circuit Complexity