With the advances of the microfluidic technology, the design of digital microfluidic biochips recently received significant attention. But thus far, the corresponding design tasks such as binding, scheduling, placement, and routing have usually been considered separately. Furthermore, often just heuristic results have been obtained. In this work, we present a one-pass synthesis scheme which directly realizes the desired functionality onto the chip and, at the same time, guarantees minimality with respect to area and/or timing. For this purpose, the deductive power of solvers for Boolean satisfiability is exploited. Experiments show how the approach leverages the design of the respective devices.
Reversible logic represents the basis for many emerging technologies and has recently been intensively studied. However, most of the Boolean functions of practical interest are irreversible and must be embedded into a reversible function before they can be synthesized. Thus far, an optimal embedding is guaranteed only for small functions, whereas a significant overhead results when large functions are considered. In this paper, we study this issue. We prove that determining an optimal embedding is coNP-hard already for restricted cases. Then, we propose heuristic and exact methods for determining both the number of additional lines as well as a corresponding embedding. For the approaches we considered sums of products and binary decision diagrams as function representations. Experimental evaluations show the applicability of the approaches for large functions. Consequently, the reversible embedding of large functions is enabled as a precursor to subsequent synthesis.
Abstract-Synthesis of reversible circuits is an active research area motivated by its applications e.g. in quantum computation or low-power design. The number of used circuit lines is thereby a crucial criterion. In this paper, we introduce several methods (including a theoretical upper bound) for the efficient computation or at least approximation of the minimal number of lines needed to realize a given function in reversible logic. While the proposed exact approach requires a significant amount of run-time (exponential in the worst case), the heuristic methods lead to very precise approximations in very short run-time. Using this, it can be shown that current synthesis approaches for large functions are still far away from producing optimal circuits with respect to the number of lines.
Abstract-Digital microfluidic biochips enable a higher degree of automation in laboratory procedures in biochemistry and molecular biology and have received significant attention in the recent past. Their design is usually conducted in several stages with routing being a particularly critical challenge. Previously proposed solutions for this design step suffer from two issues: They are mainly of heuristic nature and usually assume that the blockages to be bypassed are present the entire time. In contrast, we present a methodology which exploits the fact that blockages are often only present at certain intervals. At the same time, our approach guarantees exact solutions, i.e. always determines a routing with a minimal number of time steps. Experimental results show that, despite the huge complexity, optimal results can be achieved in reasonable run-time and that the consideration of temporary blockages indeed significantly improves the routing results.
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