Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time

Complexity of XOR/XNOR boolean functions: a model using binary decision diagrams and back propagation neural networks

This paper proposes a model that predicts the complexity of Boolean functions with only XOR/XNOR min-terms using back propagation neural networks (BPNNs) applied to Binary Decision Diagrams (BDDs). The BPNN model (BPNNM) is developed through the training process of experimental data already obtained for XOR/XNOR-based Boolean functions. The outcome of this model is a unique matrix for the complexity estimation over a set of BDDs derived from Boolean expressions with a given number of variables and XOR/XNOR min-terms. The comparison results of the experimental and BPNNM underline the efficiency of this approach, which is capable of providing some useful clues about the complexity of the circuit to be implemented. It also proves the computational capabilities of NNs in providing reliable classification of the complexity of Boolean functions.Facultad de Informátic

Cumulative dominance and heuristic performance in binary multi-attribute choice

Working paper 895, Department of Economics and Business, Universitat Pompeu FabraSeveral studies have reported high performance of simple decision heuristics in multi-attribute decision making. In this paper, we focus on situations where attributes are binary and analyze the performance of Deterministic-Elimination-By-Aspects (DEBA) and similar decision heuristics. We consider non-increasing weights and two probabilistic models for the attribute values: one where attribute values are independent Bernoulli randomvariables; the other one where they are binary random variables with inter-attribute positive correlations. Using these models, we show that good performance of DEBA is explained by the presence of cumulative as opposed to simple dominance. We therefore introduce the concepts of cumulative dominance compliance and fully cumulative dominance compliance and show that DEBA satisfies those properties. We derive a lower bound with which cumulative dominance compliant heuristics will choose a best alternative and show that, even with many attributes, this is not small. We also derive an upper bound for the expected loss of fully cumulative compliance heuristics and show that this is moderate even when the number of attributes is large. Both bounds are independent of the values of the weights.Postprint (author’s final draft

A STUDY OF BINARY DECISION DIAGRAM CHARACTERISTICS OF BENT BOOLEAN FUNCTIONS

Bent Boolean functions exist only for an even number of variables, moreover, they are unbalanced. Therefore, they are used in coding theory and in many areas of computer science. General form of bent functions is still unknown. One way of representing Boolean functions is with a reduced ordered binary decision diagram (ROBDD). The strength of ROBDDs is that they can represent Boolean functions data with a high level of redundancy in a compact form, as long as the data is encoded in such a way that the redundancy is exposed. This paper investigates characteristics of bent functions with focus on their ROBDD parameters. Decision diagram experimental framework has been used for implementation of a program for calculation of the ROBDD parameters. The results presented in this paper are intended to be used to create methods for the construction of bent functions using a ROBDD as a data structure from which the bent functions can be discovered

Modèle de contraintes temporelles pour systèmes polychrones

International audienceLa modélisation des systèmes répartis et des systèmes électroniques modernes nécessite des référentiels temporels multiples. Nous désignons ces systèmes sous le nom de “systèmes polychrones”. Le profil UML pour les systèmes temps réel et embarqués (MARTE) permet leur modélisation ainsi que la spécification de contraintes temporelles avec CCSL (Clock Constraint Specification Language). Dans MARTE, CCSL est non normatif et sa sémantique est informelle. Nous proposons ici une sémantique formelle en termes d'évolutions d'un “Time System” pour un noyau de CCSL. Un “Time System” est un modèle dynamique qui associe un ensemble de configurations à un modèle structurel constitué d'un ensemble d'horloges discrètes et de relations sur ces horloges. Les Time Systems sont comparés à d'autres modèles de causalités asynchrones, synchrones et polychrones. CCSL et sa mise en oeuvre sont illustrés sur un exemple de contrôleur d'ABS

Integrated Methodology for Software Reliability Analysis

The most used techniques to ensure safety and reliability of the systems are applied together as a whole, and in most cases, the software components are usually overlooked or to little analyzed. The present paper describes the applicability of fault trees analysis software system, analysis defined as Software Fault Tree Analysis (SFTA), fault trees are evaluated using binary decision diagrams, all of these being integrated and used with help from Java library reliability