Boolean function

Abstract: A dense and fast threshold-logic gate with a very high fan-in capacity is described. The gate performs sum-of-product and thresholding operations in an architecture comprising a poly-to-poly capacitor array and an inverter chain. The Boolean function performed by the gate is soft programmable. This is accomplished by adjusting the threshold with a dc voltage. Essentially, the operation is dynamic and thus, requires periodic reset. However, the gate can evaluate multiple input vectors in between two successive reset phases because evaluation is nondestructive. Asynchronous operation is, therefore, possible. The paper presents an electrical analysis of the gate, identifies its limitations, and describes a test chip containing four different gates of fan-in 30, 62, 127, and 255. Experimental results confirming proper functionality in all these gates are given, and applications in arithmetic and logic function blocks are described.

Abstract: A computer program, which provides bounds for system reliability, is described. The algorithms are based on the concepts of success paths and cut sets. A listing of the elements in the system, their predecessors, and the probability of successful operation of each element are the inputs. The outputs are the success paths, the cut sets, and a series of upper and lower reliability bounds; these bounds converge to the reliability which would be calculated if all the terms in the model were evaluated. The algorithm for determining the cuts from the success paths is based on Boolean logic and is relatively simple to understand. Two examples are described, one of which is very simple and the computation can be done by hand, and a second for which there are 55 success paths and 10 cuts and thus machine computation is desirable.

Abstract: We study the problem of decomposing a Boolean function into a set of functions with fewer arguments. This problem has considerable practical importance in VLSI, for example, for designs using field-programmable gate arrays. The decomposition problem is old, and well understood when the function to be decomposed is specified by a truth table, or has one output only. However, modern design tools handle functions with many outputs and represent them by cubes, for reasons of efficiency. We develop a comprehensive theory of serial decompositions for multiple-output, partially specified, Boolean functions represented by cubes. A function f (x1 , . . . , xn) has a serial decomposition if it can be expressed as h(u1 , . . . , ur, g(v1 , . . . , vs)), where U = {u1 , . . . , ur} and V = {v1 , . . . , vs} are subsets of the set X = {x1 , . . . , xn} of input variables, and g and h have fewer input variables than f. The theory uses generalized set systems (which, in turn, are generalized partitions), which we call blankets.

Abstract: Recent research shows that the class of Rotation Symmetric Boolean Functions (RSBFs), i.e., the class of Boolean functions that are invariant under circular translation of indices, is potentially rich in functions of cryptographic significance. Here we present new results regarding the Rotation Symmetric (rots) correlation immune (CI) and bent functions. We present important data structures for efficient search strategy of rots bent and CI functions. Further, we prove the nonexistence of homogeneous rots bent functions of degree ≥ 3o n a single cycle.