Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- Acknowledgments
- Contributors
- Acronyms and Abbreviations
- Boolean Models and Methods in Mathematics, Computer Science, and Engineering
- Part I Algebraic Structures
- Part II Logic
- Part III Learning Theory and Cryptography
- Part IV Graph Representations and Efficient Computation Models
- 10 Binary Decision Diagrams
- 11 Circuit Complexity
- 12 Fourier Transforms and Threshold Circuit Complexity
- 13 Neural Networks and Boolean Functions
- 14 Decision Lists and Related Classes of Boolean Functions
- Part IV Applications in Engineering
10 - Binary Decision Diagrams
from Part IV - Graph Representations and Efficient Computation Models
Published online by Cambridge University Press: 05 June 2013
- Frontmatter
- Contents
- Preface
- Introduction
- Acknowledgments
- Contributors
- Acronyms and Abbreviations
- Boolean Models and Methods in Mathematics, Computer Science, and Engineering
- Part I Algebraic Structures
- Part II Logic
- Part III Learning Theory and Cryptography
- Part IV Graph Representations and Efficient Computation Models
- 10 Binary Decision Diagrams
- 11 Circuit Complexity
- 12 Fourier Transforms and Threshold Circuit Complexity
- 13 Neural Networks and Boolean Functions
- 14 Decision Lists and Related Classes of Boolean Functions
- Part IV Applications in Engineering
Summary
Introduction
Let f: Dn → R be a finite function: that is, D and R are finite sets. Such a function can be represented by the table of all (a, f (a)), a Є Dn, which always has an exponential size of ∣D∣n. Therefore, we are interested in representations that for many important functions are much more compact. The best-known representations are circuits and decision diagrams. Circuits are a hardware model reflecting the sequential and parallel time to compute f (a) froma (see Chapter 11). Decision diagrams (DDs), also called branching programs (BPs), are nonuniform programs for computing f (a) from a based on only two types of instructions represented by nodes in a graph (see also Figure 10.1):
Decision nodes: depending on the value of some input variable xi the next node is chosen.
Output nodes (also called sinks): a value from R is presented as output.
A decision diagram is a directed acyclic graph consisting of decision nodes and output nodes. Each node v represents a function fv defined in the following way. Let a = (a1, …, an) Є Dn. At decision nodes, choose the next node as described before. The value of fv(a) is defined as the value of the output node that is finally reached when starting at v. Hence, for each node each input a Є Dn activates a unique computation path that we follow during the computation of fv(a). An edge e = (v,w) of the diagram is called activated by a if the computation path starting at v runs via e.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2010
- 1
- Cited by