The CUDD package provides functions to manipulate Binary Decision Diagrams (BDDs) [5,3], Algebraic Decision Diagrams (ADDs) [1], and Zero suppressed Decision Diagrams (ZDDs) [12]. BDDs are used to represent switch functions

In this doctoral dissertation, we study three basic problems in machine learning and two new hypothesis spaces with corresponding learning algorithms. The problems we investigate are: accuracy estimation, feature subset selection, and parameter tuning. The latter two problems are related and are studied under the wrapper approach. The hypothesis spaces we investigate are: decision tables with a default majority rule (DTMs) and oblivious read-once decision graphs (OODGs).

Knowing that some variables are symmetric in a function has numerous applications; in particular, it can help produce better variable orders for Binary Decision Diagrams (BDDs) and related data structures (e.g., Algebraic Decision Diagrams). It has been observed that there often exists an optimum order for a BDD wherein symmetric variables are contiguous. We propose a new algorithm for the detection of symmetries, based on dynamic reordering, and we study its interaction with the reordering algorithm itself. We show that combining sifting with an efficient symmetry check for contiguous variables results in the fastest symmetry detection algorithm reported to date and produces better variable orders for many BDDs. The overhead on the sifting algorithm is negligible. 1

Binary Decision Diagrams (BDDs) have gained high attention in the context of design and verification of digital circuits. They have successfully been employed to encode very large state spaces in an efficient, symbolic way. Multi terminal BDDs (MTBDDs) are generalisations of BDDs from Boolean values to values of any finite domain. In this paper, we investigate the applicability of MTBDDs to the symbolic representation of continuous time Markov chains, derived from high-level formalisms, such as queueing networks or process algebras. Based on this data structure, we discuss iterative solution algorithms to compute the steady-state probability vector that work in a completely symbolic way. We highlight a number of lessons learned, using a set of small examples.

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.

This paper describes a new BDD-based logic optimization system, BDS. It is based on a recently developed theory for BDD-based logic decomposition, which supports both algebraic and Boolean factorization. New techniques, which are crucial to the manipulation of BDDs in a partitioned Boolean network environment, are described in detail. The experimental results show that BDS has a capability to handle very large circuits. It offers a superior runtime advantage over SIS, with comparable results in terms of circuit area and often improved delay.

. We investigate the use of oblivious, read-once decision graphs as structures for representing concepts over discrete domains, and present a bottom-up, hill-climbing algorithm for inferring these structures from labelled instances. The algorithm is robust with respect to irrelevant attributes, and experimental results show that it performs well on problems considered difficult for symbolic induction methods, such as the Monk's problems and parity. 1 Introduction Top down induction of decision trees [25, 24, 20] has been one of the principal induction methods for symbolic, supervised learning. The tree structure, which is used for representing the hypothesized target concept, suffers from some wellknown problems, most notably the replication problem and the fragmentation problem [23]. The replication problem forces duplication of subtrees in disjunctive concepts, such as (A B) (C D); the fragmentation problem causes partitioning of the data into fragments, when a high-arity attrib...

The choice of a good variable ordering is crucial in applications of Ordered Binary Decision Diagrams (OBDDs). A simulated annealing approach with a new type of neighborhood is presented and analyzed. Better results as by known simulated annealing algorithms and heuristics are obtained. Some theoretical results underlining the experiments are stated.

We present a new exact algorithm for #nding the optimal variable ordering for reduced ordered Binary Decision Diagrams #BDDs#. The algorithm makes use of a lower bound technique known from VLSI design. Up to now this technique has been used only for theoretical considerations and it is adapted here for our purpose. Furthermore, the algorithm supports symmetry aspects and makes use of a hashing based data structure. Experimental results are given to demonstrate the e#ciency of our approach. We succeeded in minimizing adder functions with up to 64 variables, while all other previously presented approaches fail. 1 Introduction Recently, several design methods have been proposed that are based on ordered Binary Decision Diagrams #BDDs# #7#. The resulting circuits have very nice properties, like e.g. testability #2, 1# and lowpower #17#. For synthesis approaches based on Pass Transistor Logic #PTL# BDDs seem to be a good starting point. First promising results on how to transform a decisi...

We examine the problem of providing useful feedback to users who are denied access to resources, while controlling the disclosure of the system security policies. High-quality feedback enhances the usability of a system, especially when permissions may depend on contextual information---time of day, temperature of a room and other factors that change unpredictably. However, providing too much information to the user may breach the confidentiality of the system policies.