Abstract — Various implementations of the Quantum-dot Cellular Automata (QCA) device architecture may help many performance scaling trends continue as we approach the nanoscale. Experimental success has led to the evolution of a research track that looks at QCA-based design. The work presented in this paper follows that track and looks at implementation friendly, programmable QCA circuits. Specifically, we present a novel, QCA-based, Programmable Logic Array (PLA) structure. Our PLA is capable of providing defect tolerance at both the device and architectural level, and limits the amount of determinism required in any fabrication process. The design is compact, exploits properties unique to QCA devices in order to ease programmability, and is relevant to all implementations of QCA. I.

Abstract. In the maximum simple sharing problem (MSS), we want to compute a set of node-disjoint simple paths in an undirected bipartite graph covering as many nodes as possible of one layer of the graph, with the constraint that all paths have both endpoints in the other layer. This is a variation of the maximum sharing problem (MS) that finds important applications in the design of molecular quantum-dot cellular automata (QCA) circuits and physical synthesis in VLSI. It also generalizes the maximum weight node-disjoint path cover problem. We show that MSS is NP-complete, present a polynomial-time 5-approximation algorithm, 3 and show that it cannot be approximated with a factor better than 740 739 unless P = NP.

In the maximum sharing problem (MS), we want to compute a set of (non-simple) paths in an undirected bipartite graph covering as many nodes as possible of the first layer of the graph, with the constraint that all paths have both endpoints in the second layer and no node in that layer is covered more than once. MS is equivalent to the node-duplication based crossing elimination problem (NDCE) that arises in the design of molecular quantum-dot cellular automata (QCA) circuits and the physical synthesis of BDD based regular circuit structures in VLSI design. We show that MS is NP-hard, present a polynomial-time 1.5-approximation algorithm, and show that MS cannot be approximated with a factor better unless P = NP. than 740 739 1

This paper examines how circuits and systems made from molecular QCA devices might function. Our design constraints are “chemically reasonable ” in that we consider the characteristics and dimensions of devices and scaffoldings (circuit boards to attach devices to) that have actually been fabricated (currently in isolation). We will show that not only is the work presented here a necessary first step for any work in QCA CAD, but also that by considering issues related to design can actually help shape experiments in the physical sciences for emerging, nano-scale devices. Our work shows that circuits, scaffoldings, substrates, and devices must all be considered simultaneously. Otherwise, there is a very real possibility that the devices and scaffoldings that are eventually manufactured will result in devices that only work in isolation. This work is especially timely as experimentalists are currently working to merge the different experimental tracks – i.e. to selectively place a QCA device. 1.