Boolean function

Abstract: A nanoelectronic implementation of Boolean logic circuits is described where logic functionality is realized through charge interactions between metallic dots self-assembled on the surface of a double-barrier resonant tunneling diode (RTD) structure. The primitive computational cell in this architecture consists of a number of dots with nearest neighbor (resistive) interconnections. Specific logic functionality is provided by appropriate rectifying connections between cells. We show how basic logic gates, leading to combinational and sequential circuits, can be realized in this architecture. Additionally, architectural issues including directionality, fault tolerance, and power dissipation are discussed. Estimates based on the current-voltage characteristics of RTD's and the capacitance and resistance values of the interdot connections indicate that static power dissipation as small as 0.1 nW/gate and switching delay as small as a few picoseconds can be expected. We also present a strategy for fabricating/synthesizing such systems using chemical self-organizing/self-assembly phenomena. The proposed synthesis procedure utilizes several chemical self-assembly techniques which have been demonstrated recently, including self-assembly of uniform arrays of close-packed metallic dots with nanometer diameters, controlled resistive linking of nearest neighbor dots with conjugated organic molecules and organic rectifiers.

Abstract: Simulation by random vectors is meaningful only if the vectors meet certain requirements on the environment that drives the design under verification. When that environment is modeled by constraints, we face the problem of solving constraints efficiently. We present an efficient algorithm for simplifying conjunctive Boolean constraints defined over state and input variables, and apply it to constrained random simulation vector generation using binary decision diagrams (BDDs). The method works by extracting "hold-constraints" from the system of constraints. Hold-constraints are deterministic and trivially resolvable. They can be used to simplify the original constraints as well as refine the conjunctive partition. Experiments demonstrate significant reductions in the time and space required for constructing the conjunction BDDs, and the time spent in vector generation during simulation.

Abstract: Approximate computing is an emerging design paradigm targeting at error-tolerant applications. It trades off accuracy for improvement in hardware cost and energy efficiency. In this paper, we propose a novel approach for multi-level approximate logic synthesis under error rate constraint. The basic idea of our approach is to pick nodes in a Boolean network and shrink them by approximating their factored-form expressions. We propose two different algorithms to implement the basic idea. The first algorithm iteratively picks the most effective node at present to shrink. Its drawback lies in that it may need a large number of iterations. To overcome this drawback, the second algorithm formulates a knapsack problem to pick multiple nodes for shrinking simultaneously. It is still iterative, but the number of iterations is greatly reduced. We apply the two algorithms to MCNC benchmarks and arithmetic circuits including adders and multipliers. The experimental results demonstrated that our algorithms perform better in area saving and are 1.7 and 5.9 times faster, respectively, compared with the state-of-the-art approach.

Abstract: In this paper, we propose a novel algorithm that solves a generalized version of the Deutsch-Jozsa problem. The proposed algorithm has the potential to classify an oracle U F , that represents an unknown Boolean function on n Boolean variables, to one of 2 n different classes instead of only two classes which are constant and balanced classes in the case of Deutsch-Jozsa algorithm. The proposed algorithm is based on the use of entanglement measure to explore 2 n - 2 additional classes compared to the standard Deutsch-Jozsa algorithm. In addition, the comparison between the proposed quantum algorithm and the classical one is investigated in details. The comparison shows that the proposed algorithm is faster when the number of Boolean variables exceed 14 variables.