Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

C++ Templates as Partial Evaluation

This paper explores the relationship between C++ templates and partial evaluation. Templates were designed to support generic programming, but unintentionally provided the ability to perform compile-time computations and code generation. These features are completely accidental, and as a result their syntax is awkward. By recasting these features in terms of partial evaluation, a much simpler syntax can be achieved. C++ may be regarded as a two-level language in which types are first-class values. Template instantiation resembles an offline partial evaluator. This paper describes preliminary work toward a single mechanism based on Partial Evaluation which unifies generic programming, compile-time computation and code generation. The language Catat is introduced to illustrate these ideas.Comment: 13 page

Comparison of the Worst and Best Sum-of-Products Expressions for Multiple-Valued Functions

Because most practical logic design algorithms produce irredundant sum-of-products (ISOP) expressions, the understanding of ISOPs is crucial. We show a class of functions for which Morreale-Minato's ISOP generation algorithm produces worst ISOPs (WSOP), ISOPs with the most product terms. We show this class has the property that the ratio of the number of products in the WSOP to the number in the minimum ISOP (MSOP) is arbitrarily large when the number of variables is unbounded. The ramifications of this are significant; care must be exercised in designing algorithms that produce ISOPs. We also show that 2/sup n-1/ is a firm upper bound on the number of product terms in any ISOP for switching functions on n variables, answering a question that has been open for 30 years. We show experimental data and extend our results to functions of multiple-valued variables