Thomas Häner, Mathias Soeken
We determine the exact AND-gate cost of checking if $a\leq x < b$, where $a$ and $b$ are constant integers. Perhaps surprisingly, we find that the cost of interval checking never exceeds that of a single comparison and, in some cases, it is even lower.
Thomas Häner, Mathias Soeken
The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ is the largest number of $\land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based logic synthesis algorithm to reduce the multiplicative depth in logic networks. It makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations. Our algorithm has applications to cryptography and quantum computing, as a reduction in the multiplicative depth directly translates to a lower $T$-depth of the corresponding quantum circuit. Our experimental results show improvements in $T$-depth over state-of-the-art methods and over several hand-optimized quantum circuits for instances of AES, SHA, and floating-point arithmetic.