In Digital Image Steganography, Pixel-Value Differencing (PVD) methods use the difference between neighboring pixel values to determine the amount of data bits to be inserted. The main advantage of these methods is the size of input data that an image can hold. However, the fall-off boundary problem and the fall in error problem are persistent in many PVD steganographic methods. This results in an incorrect output image. To fix these issues, usually the pixel values are either somehow adjusted or simply not considered to carry part of the input data. In this paper, we enhance the Tri-way Pixel-Value Differencing method by finding an optimal pixel value for each pixel pair such that it carries the maximum input data possible without ignoring any pair and without yielding incorrect pixel values.

The #SAT problem is a classical #P-complete problem even for monotone, Horn and two conjunctive formulas (the last known as #2SAT). We present a novel branch and bound algorithm to solve the #2SAT problem exactly. Our procedure establishes a new threshold where #2SAT can be computed in polynomial time. We show that for any 2-CF formula F with n variables where #2SAT(F) ≤ p(n), for some polynomial p, #2SAT(F) is computed in polynomial time. This is a new way to measure the degree of difficulty for solving #2SAT and, according to such measure our algorithm allows to determine a boundary between ‘hard’ and ‘easy’ instances of the #2SAT problem.

We study a programming language with a built-in ground type for real numbers. In order for the language to be sufficiently expressive but still sequential, we consider a construction proposed by Boehm and Cartwright. The non-deterministic nature of the construction suggests the use of powerdomains in order to obtain a denotational semantics for the language. We show that the construction cannot be modelled by the Plotkin or Smyth powerdomains, but that the Hoare powerdomain gives a computationally adequate semantics. As is well known, Hoare semantics can be used in order to establish partial correctness only. Since computations on the reals are infinite, one cannot decompose total correctness into the conjunction of partial correctness and termination as it is traditionally done. We instead introduce a suitable operational notion of strong convergence and show that total correctness can be proved by establishing partial correctness (using denotational methods) and strong convergence (using operational methods). We illustrate the technique with a representative example.