This paper proposes the use of binary trees in order to represent and evaluate asymmetric decision problems with Influence Diagrams (IDs). Constraint rules are used to represent the asymmetries between the variables of the ID. These rules and the potentials involved in IDs will be represented using binary trees. The application of these rules can reduce the size of the potentials of the ID. As ...

A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0, 1}n → Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions ...

We explore the criteria that contribute to the validity of modeling structures within the entity-relationship (ER) diagram. Our approach examines cardinality constraints in conjunction with the degree of the relationship to address constraint consistency and role uniqueness issues. Here we use both maximum and minimum cardinality constraints yielding a complete analysis of the structural validi...

We present a data structure | the Mod{2{OBDD's that considerably extend OBDD's (ordered binary decision diagrams) as well as ESOP's (EXOR{sum{of{ products). Many Boolean function of practical interest like hidden weighted bit function, indirect storage access function, important symmetric functions have exponential size optimal OBDD's and/or ESOP's (even multilevel EXOR{expressions) but (low de...

In this paper we propose a new algorithm for solving general two-player turn-taking games that performs symbolic search utilizing binary decision diagrams (BDDs). It consists of two stages: First, it determines all breadth-first search (BFS) layers using forward search and omitting duplicate detection, next, the solving process operates in backward direction only within these BFS layers thereby...

This paper considers the diagnosis of large discrete-event systems consisting of many components. The problem is to determine, online, all failures and states that explain a given sequence of observations. Several model-based diagnosis approaches deal with this problem but they usually have either poor time performance or result in space explosion. Recent work has shown that both problems can b...

We introduce a BDD with redundant variables as an Indexed BDD(IBDD) and define PolyIBDD as the class of Boolean functions represented by polynomial-sized IBDDs or the $\mathfrak{n}tltll$ ber of input variables. Assuming that the class of languages on $\{0,1\}$ that are accepted by logarithmic space bounded DTMs is DLOG, $\downarrow$ he f'ollowing relation holds. PolyIBDD $=DLOG$. That is to say...

We present algorithms for partially observable planning that iteratively compute belief states with an increasing distance to the goal states. The algorithms handle nondeterministic operators, but restrict to problem instances with a finite upper bound on execution length, that is plans without loops. We discuss an implementation of the algorithms which uses binary decision diagrams for represe...

This paper introduces two new methods for observing and recording the vectors that have been asserted on a bus. The first is a software approach that uses a novel data structure similar to binary decision diagrams which allows for a compact representation of stored values. Even though the new data structure presented in this paper can potentially grow to contain just as many nodes as there are ...

In this article, we disprove the long-standing conjecture, proposed by R. E. Bryant in 1986, that his binary decision diagram (BDD) algorithm computes any binary operation on two Boolean functions in linear time in the input-output sizes. We present Boolean functions for which the time required by Bryant’s algorithm is a quadratic of the input-output sizes for all nontrivial binary operations, ...