Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structured decomposition for reversible Boolean functions   Reversible Boolean function is a one-to-one function which maps $n$-bit input
to $n$-bit output. Reversible logic synthesis has been widely studied due to
its relationship with low-energy computation as well as quantum computation. In
this work, we give a structured decomposition for even reversible Boolean
functions (RBF). Specifically, for $n\geq 6$, any even $n$-bit RBF can be
decomposed to $7$ blocks of $(n-1)$-bit RBF, where $7$ is a constant
independent of $n$; and the positions of those blocks have large degree of
freedom. Moreover, if the $(n-1)$-bit RBFs are required to be even as well, we
show for $n\geq 10$, $n$-bit RBF can be decomposed to $10$ even $(n-1)$-bit
RBFs. For simplicity, we say our decomposition has block depth $7$ and even
block depth $10$.
  Our result improves Selinger's work in block depth model, by reducing the
constant from $9$ to $7$; and from $13$ to $10$ when the blocks are limited to
be even. We emphasize that our setting is a bit different from Selinger's. In
Selinger's constructive proof, each block is one of two specific positions and
thus the decomposition has an alternating structure. We relax this restriction
and allow each block to act on arbitrary $(n-1)$ bits. This relaxation keeps
the block structure and provides more candidates when choosing positions of
blocks.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
9
The categories of this paper are: nlin