COMPACT: Flow-Based Computing on Nanoscale Crossbars With Minimal Semiperimeter and Maximum Dimension

Abstract

In-memory computing is a promising solution strategy for data-intensive applications to circumvent the von Neumann bottleneck. Flow-based computing is the concept of performing in-memory computing using sneak paths in nanoscale crossbar arrays. The limitation of the previous work is that the resulting crossbar representations have large size. In this article, we present a framework called COMPACT for mapping Boolean functions to crossbar representations with a minimal semiperimeter (the number of wordlines plus bitlines) and/or maximum dimension (the maximum of the wordlines or bitlines). The COMPACT framework is based on an analogy between binary decision diagrams (BDDs) and nanoscale memristor crossbar arrays. More specifically, nodes and edges in a BDD correspond to wordlines/bitlines and memristors in a crossbar array, respectively. The relation enables a Boolean function represented by a BDD with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> nodes and an odd cycle transversal of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> to be mapped to a crossbar with a semiperimeter of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n+k$ </tex-math></inline-formula> . The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> extra wordlines/bitlines are introduced due to crossbar connection constraints, i.e., wordlines (bitlines) cannot directly be connected to wordlines (bitlines). Moreover, there exists a tradeoff between the semiperimeter and maximum dimension. Consequently, COMPACT can sometimes reduce the maximum dimension by slightly increasing the length of the semiperimeter. We also extend COMPACT to handle multioutput functions using shared BDD (SBDDs) and alignment constraints on the inputs and outputs. Compared with the state-of-the-art mapping technique, the semiperimeter and maximum dimension are reduced by 55% and 85%, respectively. The area, power consumption, and computation delay are reduced by 89%, 19%, 56%, respectively.