This paper describes a new data structure called the \Haar Spectral Diagram" (or HSD) useful for representing the Haar spectrum of boolean functions. An alternative ordering of Haar coe cients is used to represent the Haar transform matrix in terms of a Kronecker product yielding a natural decision-diagram based representation. The resulting graph is a pointdecomposition of the Haar spectrum us...

Reduced Ordered Binary Decision Diagrams (ROBDDs) gained widespread use in logic design verification, test generation, fault simulation, and logic synthesis [17, 7]. Since the size of an ROBDD heavily depends on the variable order used, there is a strong need to find variable orders that minimize the number of nodes in an ROBDD. In certain applications we have to cope with ROBDDs with different...

The paper identifies patterns of Boolean variables that occur in Boolean formulae, namely AND-clusters and OR-clusters. We give a polynomial algorithm that detects AND-clusters in disjunctive normal form (DNF) Boolean formulae, or OR-clusters in conjunctive normal form (CNF) Boolean formulae. Furthermore, we explain how to exploit the clusters in the context of ProbLog. In ProbLog, Boolean form...

The size of a Reduced Ordered Binary Decision Diagram (ROBDD) is directly influenced by the variables ordering technique used to build the ROBDD. Therefore various variables ordering techniques have been proposed to minimize the size of BDDs. Unfortunately there is no unique method that can be used to obtain the least number of nodes for all BDDs. In this paper we propose two new methods based ...

This paper presents an implementation of the ROBDD data structure in Haskell. It shows that lazy evaluation can be used to improve the performance of some ROBDD algorithms. While standard implementations construct the whole structure no matter which parts are demanded we use lazy evaluation to provide a more demand driven construction. To achieve this behavior we have to relax a property that g...

Constraint solvers typically maintain a domain of possible values for each variable that may form part of a solution to a constraint satisfaction problem. Historically, it has been thought impractical to represent precisely the domains of certain types of constrained variable, such as finite set variables. For example, the domain of a finite set variable which can take on the value of any subse...

In this paper we develop a combinatorial method for the evaluation of yield of fault-tolerant systems-on-chip. The method assumes that defects are produced according to a model in which defects are lethal and affect given components of the system following a distribution common to all defects. The distribution of the number of defects is arbitrary. The method is based on the formulation of the ...

This paper presents a heuristic algorithm for disjoint decomposition of a Boolean function based on its ROBDD representation. Two distinct features make the algorithm feasible for large functions. First, for an n-variable function, it checks only O(n2) candidates for decomposition out of O(2n) possible ones. A special strategy for selecting candidates makes it likely that all other decompositio...

We present a method computing a minimum sized partition of the variables of an incompletely specied Boolean function into symmetric groups. The method can be used during minimization of robdds of incompletely speci ed Boolean functions. We apply it as a preprocessing step of symmetric sifting presented by Panda [24] and Moller [20] and of techniques for robdd minimization of incompletely speci...

We identify two families of canonical knowledge compilation languages. Both families augment ROBDD with conjunctive decomposition bounded by an integer i ranging from 0 to ∞. In the former, the decomposition is finest and the decision respects a chain C of variables, while both the decomposition and decision of the latter respect a tree T of variables. In particular, these two families cover th...