Frequently, randomly organized data is needed to avoid an anomalous operation of other algorithms and computational processes. An analogy is that a deck of cards is ordered within the pack, but before a game of poker or solitaire the deck is shuffled to create a random permutation. Shuffling is used to assure that an aggregate of data elements for a sequence S is randomly arranged, but avoids a...

In the field of hardware and software verification, many applications require to determine satisfiability of first-order-logic with respect to one or more background theories, also referred to as Satisfiability Modulo Theories (SMT). The majority of these applications relies on bit-precise reasoning as provided by SMT solvers for the quantifier-free theory of fixed-size bit-vectors, often combi...

In many applications, such as inverse dithering, it is necessary to increase the pixel bit-depth of images by expanding q -bit integer values to m -bit integer values ( q m > ). This paper describes a simple and efficient method that uses bit replication, instead of conventional multiplication, to achieve this expansion. First, we show that the optimal number of repetitions is given by } / { ce...