Boolean Expression Diagrams

This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One is a generalized version of the BDD apply-operator while the other can exploit the structural information of the Boolean expression. This ability is demonstrated by verifying that two di erent circuit implementations of a 16-bit multiplier implement the same Boolean function. Using BEDs, this veri cation problem is solved in less than a second, while using standard BDD techniques this problem is infeasible. Generally, BEDs are useful in applications, for example tautology checking, where the end-result as a reduced ordered BDD is small

A graphical user interface for Boolean query specification

On-line information repositories commonly provide keyword search facilities via textual query languages based on Boolean logic. However, there is evidence to suggest that the syntactical demands of such languages can lead to user errors and adversely affect the time that it takes users to form queries. Users also face difficulties because of the conflict in semantics between AND and OR when used in Boolean logic and English language. We suggest that graphical query languages, in particular Venn-like diagrams, can alleviate the problems that users experience when forming Boolean expressions with textual languages. We describe Vquery, a Venn-diagram based user interface to the New Zealand Digital Library (NZDL). The design of Vquery has been partly motivated by analysis of NZDL usage. We found that few queries contain more than three terms, use of the intersection operator dominates and that query refinement is common. A study of the utility of Venn diagrams for query specification indicates that with little or no training users can interpret and form Venn-like diagrams which accurately correspond to Boolean expressions. The utility of Vquery is considered and directions for future work are proposed

Using formal metamodels to check consistency of functional views in information systems specification

UML notations require adaptation for applications such as Information Systems (IS). Thus we have defined IS-UML. The purpose of this article is twofold. First, we propose an extension to this language to deal with functional aspects of IS. We use two views to specify IS transactions: the first one is defined as a combination of behavioural UML diagrams (collaboration and state diagrams), and the second one is based on the definition of specific classes of an extended class diagram. The final objective of the article is to consider consistency issues between the various diagrams of an IS-UML specification. In common with other UML languages, we use a metamodel to define IS-UML. We use class diagrams to summarize the metamodel structure and a formal language, B, for the full metamodel. This allows us to formally express consistency checks and mapping rules between specific metamodel concepts. (C) 2007 Elsevier B.V. All rights reserved

An algorithm for the synthesis of NAND logic networks using a diagrammatic approach

A diagrammatic approach is presented for the synthesis of multilevel NAND networks realizing combinational logic expressions. The network synthesized is restricted to only uncomplemented inputs. The synthesis algorithm involves the determination of minimum sum of products and product of sums expressions for a Boolean function, construction of an α-ß diagram from these expressions followed by implementation with NAND gates directly from the diagram. The resulting network is a minimal or near minimal NAND gate realization of the given function. The algorithm is applicable to completely or incompletely specified Boolean functions and is extended to include NOR synthesis --Abstract, page 2

Metamodel-based model conformance and multiview consistency checking

Model-driven development, using languages such as UML and BON, often makes use of multiple diagrams (e.g., class and sequence diagrams) when modeling systems. These diagrams, presenting different views of a system of interest, may be inconsistent. A metamodel provides a unifying framework in which to ensure and check consistency, while at the same time providing the means to distinguish between valid and invalid models, that is, conformance. Two formal specifications of the metamodel for an object-oriented modeling language are presented, and it is shown how to use these specifications for model conformance and multiview consistency checking. Comparisons are made in terms of completeness and the level of automation each provide for checking multiview consistency and model conformance. The lessons learned from applying formal techniques to the problems of metamodeling, model conformance, and multiview consistency checking are summarized