If \(X\) and \(Y\) are the inputs, the given circuit works as _______.

The circuit consists of four NAND gates.

The first two NAND gates have their inputs tied together, acting as NOT gates. Their outputs are \(\overline{X}\) and \(\overline{Y}\).

These outputs are fed into the third NAND gate. The output of this gate is:
\(y' = \overline{\overline{X} \cdot \overline{Y}}\)

Using De Morgan's theorem:
\(y' = \overline{\overline{X}} + \overline{\overline{Y}} = X + Y\)

This output is fed into the fourth NAND gate, which also has its inputs tied together, acting as a NOT gate. The final output is:
Output \(= \overline{X + Y}\)

This represents the Boolean expression for a NOR gate.

Answer: NOR gate