Shin-ichi Minato

Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems

In this paper, we propose Zero-Suppressed BDDs (0-Sup-BDDs), which are BDDs based on a new reduction rule. This data structure brings unique and compact representation of sets which appear in many combinatorial problems. Using 0-Sup-BDDs, we can manipulate such sets more simply and efficiently than using original BDDs. We show the properties of 0-Sup-BDDs, their manipulation algorithms, and good applications for LSI CAD systems.

Binary decision diagrams and applications for VLSI CAD

Foreword. Preface. 1. Introduction. 2. Techniques of BDD manipulation. 3. Variable ordering for BDDs. 4. Representation of multi-valued functions. 5. Generation of cube sets from BDDs. 6. Zero-suppressed BDDs. 7. Multi-level logic synthesis using ZBDDs. 8. Implicit manipulation of polynomials based on ZBDDs. 9. Arithmetic Boolean expressions. 10. Conclusions. References. Index.

Zero-suppressed BDDs and their applications

Abstract.In many real-life problems, we are often faced with manipulating sets of combinations. In this article, we study a special type of ordered binary decision diagram (OBDD), called zero-suppressed BDDs (ZBDDs). This data structure represents sets of combinations more efficiently than using original OBDDs. We discuss the basic data structures and algorithms for manipulating ZBDDs in contrast with the original OBDDs. We also present some practical applications of ZBDDs, such as solving combinatorial problems with unate cube set algebra, logic synthesis methods, Petri net processing, etc. We show that a ZBDD is a useful option in OBDD techniques, suitable for a part of the practical applications.

Graph-Based Representations of Discrete Functions

BDDs are now commonly used for representing Boolean functions because of their efficiency in terms of time and space. There are many cases in which conventional algorithms can be significantly improved by using BDDs. Recently, several variants of BDDs have been developed to represent other kinds of discrete functions, such as multi-valued functions, cube sets, or arithmetic formulas. These techniques are useful not only for VLSI CAD but also for various areas in Computer Science. In this chapter, we survey the techniques of BDD and its variants. We explain the basic method of BDD manipulation, and show the relationships between the different types of BDDs.

Finding all simple disjunctive decompositions using irredundant sum-of-products forms

Finding disjunctive decompositions is an important technique to realize compact logic networks. Simple disjunctive decomposition is a basic and useful concept, that extracts a single output subblock function whose input variable set is disjunctive from the other part. The paper presents a method for finding simple disjunctive decompositions by generating irredundant sum-of-products forms and applying factorization. We prove that all simple disjunctive decompositions can be extracted in our method, namely all possible decompositions are included in the factored logic networks. Experimental results show that our method can efficiently extract all the simple disjunctive decompositions of the large scale functions. Our result clarifies the relationship between the functional decomposition method and the two-level logic factorization method.

Distribution Loss Minimization With Guaranteed Error Bound

Determining loss minimum configuration in a distribution network is a hard discrete optimization problem involving many variables. Since more and more dispersed generators are installed on the demand side of power systems and they are reconfigured frequently, developing automatic approaches is indispensable for effectively managing a large-scale distribution network. Existing fast methods employ local updates that gradually improve the loss to solve such an optimization problem. However, they eventually get stuck at local minima, resulting in arbitrarily poor results. In contrast, this paper presents a novel optimization method that provides an error bound on the solution quality. Thus, the obtained solution quality can be evaluated in comparison to the global optimal solution. Instead of using local updates, we construct a highly compressed search space using a binary decision diagram and reduce the optimization problem to a shortest path-finding problem. Our method was shown to be not only accurate but also remarkably efficient; optimization of a large-scale model network with 468 switches was solved in three hours with 1.56% relative error bound.

BDDs vs. Zero-Suppressed BDDs: for CTL Symbolic Model Checking of Petri Nets

This paper proposes using Zero-Suppressed BDDs for the CTL symbolic model checking of Petri nets. Since the state spaces of Petri nets are often very sparse, it is expected that ZBDDs represent such sparse state spaces more efficiently than BDDs. Further, we propose special BDD/ZBDD operations for Petri nets which accelerate the manipulations of Petri nets. The approaches to handling Petri nets based on BDDs and ZBDDs are compared with several example nets, and it is shown that ZBDDs are more suitable for the symbolic manipulation of Petri nets.

Implicit manipulation of polynomials using zero-suppressed BDDs

We present a new technique that broadens the scope of BDD application. It involves manipulating arithmetic polynomials containing higher-degree variables and integer coefficients. Our method can represent large-scale polynomials compactly and uniquely, and it greatly accelerates computation of polynomials. As the polynomial calculus is a basic model in mathematics, our method is very useful in various areas, including formal verification techniques for VLSI design.<<ETX>>

Fast factorization method for implicit cube set representation

This paper presents a fast weak-division method for implicit cube set representation using Zero-Suppressed Binary Decision Diagrams, which are a new type of Binary Decision Diagram adapted for representing sets of combinations. Our new weak-division algorithm can be executed in a time almost proportional to the size of the graph, regardless of the number of cubes and literals. Based on this technique, we implemented a simple program for optimizing multilevel logic circuits. Experimental results indicate that we can quickly flatten and factorize multilevel logics even for parity functions and full adders, which have never been flattened in other methods. Our method greatly accelerates multilevel logic synthesis systems and enlarges the scale of applicable circuits.

Calculation of Unate Cube Set Algebra Using Zero-Suppressed BDDs

Many combinatorial problems in LSI design can be described with cube set expressions. We discuss unate cube set algebra based on zero-suppressed BDDs, a new type of BDDs adapted for cube set manipulation. We propose efficient algorithms for computing unate cube set operations including multiplication and division, followed by some practical applications of unate cube set calculation.