Iterative Logic Arrays (ILAs) are ideal as VLSI sub-systems because of their regular structure and its close resemblance with FPGAs (Field Programmable Gate Arrays). Reversible circuits are of interest in the design of very low power circuits where e
nergy loss implied by high frequency switching is not of much consideration. Reversibility is essential for Quantum Computing. This paper examines the testability of Reversible Iterative Logic Arrays (ILAs) composed of reversible k-CNOT gates. For certain ILAs it is possible to find a test set whose size remains constant irrespective of the size of the ILA, while for others it varies with array size. Former type of ILAs is known as Constant-Testable, i.e. C-Testable. It has been shown that Reversible Logic Arrays are C-Testable and size of test set is equal to number of entries in cells truth table implying that the reversible ILAs are also Optimal-Testable, i.e. O-Testable. Uniform-Testability, i.e. U-Testability has been defined and Reversible Heterogeneous ILAs have been characterized as U-Testable. The test generation problem has been shown to be related to certain properties of cycles in a set of graphs derived from cell truth table. By careful analysis of these cycles an efficient test generation technique that can be easily converted to an ATPG program has been presented for both 1-D and 2D ILAs. The same algorithms can be easily extended for n-Dimensional Reversible ILAs.
We study the basin of attraction of static extremal black holes, in the concrete setting of the STU model. By finding a connection to a decoupled Toda-like system and solving it exactly, we find a simple way to characterize the attraction basin via c
ompeting behaviors of certain parameters. The boundaries of attraction arise in the various limits where these parameters degenerate to zero. We find that these boundaries are generalizations of the recently introduced (extremal) subtracted geometry: the warp factors still exhibit asymptotic integer power law behaviors, but the powers can be different from one. As we cross over one of these boundaries (generalized subttractors), the solutions turn unstable and start blowing up at finite radius and lose their asymptotic region. Our results are fully analytic, but we also solve a simpler theory where the attraction basin is lower dimensional and easy to visualize, and present a simple picture that illustrates many of the basic ideas.
We consider extremal limits of the recently constructed subtracted geometry. We show that extremality makes the horizon attractive against scalar perturbations, but radial evolution of such perturbations changes the asymptotics: from a conical-box to
flat Minkowski. Thus these are black holes that retain their near-horizon geometry under perturbations that drastically change their asymptotics. We also show that this extremal subtracted solution (subttractor) can arise as a boundary of the basin of attraction for flat space attractors. We demonstrate this by using a fairly minimal action (that has connections with STU model) where the equations of motion are integrable and we are able to find analytic solutions that capture the flow from the horizon to the asymptotic region. The subttractor is a boundary between two qualitatively different flows. We expect that these results have generalizations for other theories with charged dilatonic black holes.
Reversible circuits find applications in many areas of Computer Science including Quantum Computation. This paper examines the testability of an important subclass of reversible logic circuits that are composed of k-wire controlled NOT (k-CNOT with k
>/- 1) gates. A reversible k-CNOT gate can be implemented using an irreversible k-input AND gate and an EXOR gate. A reversible k-CNOT circuit where each k-CNOT gate is realized using irreversible k-input AND and EXOR gate, has been considered. One of the most commonly used Single Bridging Fault model (both wired-AND and wired-OR) has been assumed to be type of fault for such circuits. It has been shown that an (n+p)-input AND-EXOR based reversible logic circuit with p observable outputs, can be tested for single bridging faults (SBF) using (3n + lefthalfcap log2p righthalfcap + 2) tests.
