Reversible logic synthesis

• Authors: Gerhard W. Dueck;Dmitri Aleksandrovich Maslov
• Venue: Reversible logic synthesis
• Year: 2003

Reversible logic is an emerging research area. Interest in reversible logic is sparked by its necessity in quantum technologies. Reversible implementations are also found in optical technology, nanotechnology, thermodynamics and adiabatic CMOS. Power dissipation in modern technologies is an important issue, and overheating is a serious concern for both manufacturer (impossibility of introducing new, smaller scale technologies, limited temperature range for operating the product) and customer (power supply, which is especially important for mobile systems). One of the main benefits that reversible logic brings is theoretically zero power dissipation in the sense that, independently of underlying technology, irreversibility means heat generation. Most of the listed technologies are either emerging or not fully investigated. As a result, only a small number of Boolean functions can be computed using hardware based on reversible technology. Part of this problem comes from the incompleteness of the technological results, the other part arises from absence of good circuit synthesis procedures. Synthesis of multiple-output functions has to be done in terms of reversible objects. This usually results in addition of garbage bits (bits needed for reversibility, but not required for the output part of a circuit), which in contrast to the non-reversible case is technologically difficult and expensive. The situation is rather pessimistic when it is observed that proposed synthesis procedures use excessive garbage. The amount of garbage is a very important criterion for a good synthesis procedure, since in most technologies the addition of only one bit of garbage is expensive or even impossible to implement. Based on this information, a crucial way to help reversible logic to evolve and become usable is to design a synthesis method which uses the theoretically minimal number of garbage bits. This will help the emerging technologies to use the results of reversible synthesis even in the early stage of their development. Minimal garbage realization may require a larger number of gates in the circuit, but it is better to have a large but working circuit than a small one that is not ready for the technology. In this thesis several synthesis methods that use minimal garbage are considered: RCMG model (defined as a part of this thesis), Toffoli synthesis, Fredkin/Toffoli synthesis. Dynamic programming algorithms are synthesized separately with near minimal garbage. Some of the methods use minimal garbage and produce small circuits (Toffoli and Fred-kin/Toffoli synthesis) but work with reversible specifications, some handle “don't cares” (RCMG), some even allow a trade-off between the garbage amount and the number of gates in the resulting circuit. When a technology is chosen and the relationship between costs of one bit of garbage and a single gate is specified, one or the other method may be better. In the presented thesis the main goal is to design synthesis methods that will be suitable for different cost distributions.