Combinational multiple-valued circuit design by generalised disjunctive decomposition

A design of multiple-valued circuits based on the multiple-valued programmable logic arrays (MV PLA’s) by generalized disjunctive decomposition is presented. Main subjects are 1) Generalized disjunctive decomposition of multiple-valued functions using multiple-terminal multiplevalued decision diagrams (MTMDD’s); 2) Realization of functions by MV PLA-based combinatorial circuits

Computer program detects transient malfunctions in switching circuits

A program which accepts a system model in the form of Boolean equations and solves these equations using a ternary algebra will determine the response of large combinational and sequencial switching circuits to given input changes, taking into account malfunctions due to races, hazards, and oscillations

Finite Type Invariants of w-Knotted Objects II: Tangles, Foams and the Kashiwara-Vergne Problem

This is the second in a series of papers dedicated to studying w-knots, and more generally, w-knotted objects (w-braids, w-tangles, etc.). These are classes of knotted objects that are wider but weaker than their "usual" counterparts. To get (say) w-knots from usual knots (or u-knots), one has to allow non-planar "virtual" knot diagrams, hence enlarging the the base set of knots. But then one imposes a new relation beyond the ordinary collection of Reidemeister moves, called the "overcrossings commute" relation, making w-knotted objects a bit weaker once again. Satoh studied several classes of w-knotted objects (under the name "weakly-virtual") and has shown them to be closely related to certain classes of knotted surfaces in R4. In this article we study finite type invariants of w-tangles and w-trivalent graphs (also referred to as w-tangled foams). Much as the spaces A of chord diagrams for ordinary knotted objects are related to metrized Lie algebras, the spaces Aw of "arrow diagrams" for w-knotted objects are related to not-necessarily-metrized Lie algebras. Many questions concerning w-knotted objects turn out to be equivalent to questions about Lie algebras. Most notably we find that a homomorphic universal finite type invariant of w-foams is essentially the same as a solution of the Kashiwara-Vergne conjecture and much of the Alekseev-Torossian work on Drinfel'd associators and Kashiwara-Vergne can be re-interpreted as a study of w-foams.Comment: 57 pages. Improvements to the exposition following a referee repor

Online self-repair of FIR filters

Chip-level failure detection has been a target of research for some time, but today's very deep-submicron technology is forcing such research to move beyond detection. Repair, especially self-repair, has become very important for containing the susceptibility of today's chips. This article introduces a self-repair-solution for the digital FIR filter, one of the key blocks used in DSPs