3 research outputs found
Fast Adjustable NPN Classification Using Generalized Symmetries
NPN classification of Boolean functions is a powerful technique used in many logic synthesis and technology mapping tools in FPGA design flows. Computing the canonical form of a function is the most common approach of Boolean function classification. In this paper, a novel algorithm for computing NPN canonical form is proposed. By exploiting symmetries under different phase assignments and higher-order symmetries of Boolean functions, the search space of NPN canonical form computation is pruned and the runtime is dramatically reduced. The algorithm can be adjusted to be a slow exact algorithm or a fast heuristic algorithm with lower quality. For exact classification, the proposed algorithm achieves a 30× speedup compared to a state-of-the-art algorithm. For heuristic classification, the proposed algorithm has similar performance as the state-of-the-art algorithm with a possibility to trade runtime for quality
Symmetry Properties of Nested Canalyzing Functions
Many researchers have studied symmetry properties of various Boolean
functions. A class of Boolean functions, called nested canalyzing functions
(NCFs), has been used to model certain biological phenomena. We identify some
interesting relationships between NCFs, symmetric Boolean functions and a
generalization of symmetric Boolean functions, which we call -symmetric
functions (where is the symmetry level). Using a normalized representation
for NCFs, we develop a characterization of when two variables of an NCF are
symmetric. Using this characterization, we show that the symmetry level of an
NCF can be easily computed given a standard representation of . We also
present an algorithm for testing whether a given -symmetric function is an
NCF. Further, we show that for any NCF with variables, the notion of
strong asymmetry considered in the literature is equivalent to the property
that is -symmetric. We use this result to derive a closed form
expression for the number of -variable Boolean functions that are NCFs and
strongly asymmetric. We also identify all the Boolean functions that are NCFs
and symmetric.Comment: 17 page