#### DMCA

## Decision Diagram Optimization Using Copy Properties

### Citations

3470 | Graph-based algorithms for boolean function manipulation
- Bryant
- 1986
(Show Context)
Citation Context ...n extended library of relationships between sequences producing isomorphic subtrees permitting reduction of DTs and resulting in more compact DDs. 2. Background Theory Binary Decision Diagrams (BDDs) =-=[1]-=- are defined by using the Shannon expansion rule £���� � © £���� � © £�� , where . £�� and £�� are co-factors of £ for � © ��� and � © ��� , respectively. In a BDD, we denote outgoing � edges £�� of £... |

498 | Efficient implementation of a bdd package
- Brace, Rudell, et al.
- 1991
(Show Context)
Citation Context ...cess¨§�©�� ins¢¡¤£¦¥ , since such subsequences result in appearance of isomorphic subtrees in the DT. Smallest isomorphic subtrees are constant nodes showing equal values. DDs with complemented edges =-=[2]-=- are a generalization derived by considering as isomorphic subtrees representing subsequencess�§�©��s�§�©�� and . The sign minus is considered � as logic negation in bit-level DDs, and as arithmetic n... |

272 | Cudd: Cu decision diagram package release 2.3.0
- Somenzi
- 1998
(Show Context)
Citation Context ...e operations of reversing and negation of function values over subgraphs. 8. Experimental Results For the experimental estimation of properties of CDDs, we developed a program in the CUDD environment =-=[8]-=-, for transforming MTBDDs into CDDs and HCDDs. The size of CDDs and the corresponding MTBDDs from which they are derived for some benchmark functions are given in Table 2. The used benchmark functions... |

184 |
Multiterminal binary decision diagrams: an efficient data structure for matrix representation
- Fujita, McGeer, et al.
- 1997
(Show Context)
Citation Context ...en Faculty of Electronic Eng. Inst. of Computer Science Yugoslavia Germany Abstract In this paper, we propose an approach to the reduction of sizes of Multi-Terminal Binary Decision Diagrams (MTBDDs) =-=[3]-=- by using the copy properties of discrete functions. The underlying principles come from copy theory of discrete signals considered in [5, 6, 7]. We propose two modifications of MTBDDs, called Copy DD... |

5 |
Ordering of Walsh functions
- Zhihua, Qishan
- 1983
(Show Context)
Citation Context ...����� ��� � ������� ������� For application of copy operations to the subtrees rooted at the nodes at upper levels in the MTBDD, we use the second-order operators defined as follows [11], [10], [12], =-=[13]-=-. Definition 5 Let � be a sequence of complex numbers. The operators � , � , and � � are defined by ��� � ��� � � �s��� ¡ � ¥ � � � � � � ¡ � � � � � � ¥��¡s� where stands for the reversed � sequence ... |

3 |
Complex Bridge functions
- Stanković, Zhang
- 1994
(Show Context)
Citation Context ...� ��� ����� ����� ��� � ������� ������� For application of copy operations to the subtrees rooted at the nodes at upper levels in the MTBDD, we use the second-order operators defined as follows [11], =-=[10]-=-, [12], [13]. Definition 5 Let � be a sequence of complex numbers. The operators � , � , and � � are defined by ��� � ��� � � �s��� ¡ � ¥ � � � � � � ¡ � � � � � � ¥��¡s� where stands for the reversed... |

2 |
Fourier decision diagrams on finite non-Abelian groups with preprocessing
- Stanković
- 1997
(Show Context)
Citation Context ..., it has been suggested to use for � also the multiplication ��� with ¡ the ��¥ complex unity , complex-conjugation and proper� � ties of symmetry, sqew-symmetry, and Hermitean properties of matrices =-=[9]-=-. In matrix-valued Fourier DDs, � is extended to consider as isomorphic the subtrees representing the complex-conjugate transpose matrices, Hermitean matrices. In optimization of MTBDDs with copy oper... |

2 |
Introduction to bridge functions
- Zhihua, Qishan
- 1983
(Show Context)
Citation Context ...����� ����� ��� � ������� ������� For application of copy operations to the subtrees rooted at the nodes at upper levels in the MTBDD, we use the second-order operators defined as follows [11], [10], =-=[12]-=-, [13]. Definition 5 Let � be a sequence of complex numbers. The operators � , � , and � � are defined by ��� � ��� � � �s��� ¡ � ¥ � � � � � � ¡ � � � � � � ¥��¡s� where stands for the reversed � seq... |

1 |
Dual edge operations in reduced ordered binary decision diagrams
- Miller, Drechsler
- 1998
(Show Context)
Citation Context ... edge. � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � It should be noted that HCDDs for Boolean functions are similar to BDDs with dual edges or dual markers as considered in =-=[4]-=-. 5. Examples In this section, we give some examples of functions that have copy properties. Such functions can be efficiently represented by CDDs and HCDDs. We define the rules for the generation of ... |

1 |
Copy Theory of Signals and Its Applications
- Minglu, Qishan
- 1996
(Show Context)
Citation Context ... of sizes of Multi-Terminal Binary Decision Diagrams (MTBDDs) [3] by using the copy properties of discrete functions. The underlying principles come from copy theory of discrete signals considered in =-=[5, 6, 7]-=-. We propose two modifications of MTBDDs, called Copy DDs (CDDs) and Half Copy DDs (HCDDs), using the corresponding copy operations from copy theory. Functions having different types of copy propertie... |

1 |
Shift copy analysis of signals
- Minglu, Qishan
- 1994
(Show Context)
Citation Context ... of sizes of Multi-Terminal Binary Decision Diagrams (MTBDDs) [3] by using the copy properties of discrete functions. The underlying principles come from copy theory of discrete signals considered in =-=[5, 6, 7]-=-. We propose two modifications of MTBDDs, called Copy DDs (CDDs) and Half Copy DDs (HCDDs), using the corresponding copy operations from copy theory. Functions having different types of copy propertie... |

1 |
A summary of Bridge functions”, in Recent Developments in Abstract Harmonic Analysis with Applications
- Qishan
- 1996
(Show Context)
Citation Context ... of sizes of Multi-Terminal Binary Decision Diagrams (MTBDDs) [3] by using the copy properties of discrete functions. The underlying principles come from copy theory of discrete signals considered in =-=[5, 6, 7]-=-. We propose two modifications of MTBDDs, called Copy DDs (CDDs) and Half Copy DDs (HCDDs), using the corresponding copy operations from copy theory. Functions having different types of copy propertie... |

1 |
A group of three-valued functions
- Zhang, Zhijing
- 1990
(Show Context)
Citation Context ...e matrices, Hermitean matrices. In optimization of MTBDDs with copy operations, we consider as isomorphic subtrees representing £ � � � ��¡�£¦¥ and , where is an operator in the set of copy operators =-=[11]-=- defined below. 2.1. Copy Operations In this section, we briefly present the basic notions from copy theory [5]. As it is pointed out in [5], the copy feature is an important property of discrete sign... |