## Antisymmetries in the realization of Boolean functions

Venue: | in Proc. Int. Symp. on Circuits and Systems, ISCAS 2002, Scottsdale Princess Resort |

Citations: | 1 - 0 self |

### BibTeX

@INPROCEEDINGS{Rice_antisymmetriesin,

author = {J. E. Rice and J. C. Muzio},

title = {Antisymmetries in the realization of Boolean functions},

booktitle = {in Proc. Int. Symp. on Circuits and Systems, ISCAS 2002, Scottsdale Princess Resort},

year = {},

pages = {2666}

}

### OpenURL

### Abstract

New symmetries of degree two are introduced, along with spectral techniques for identifying these symmetries. Some applications of these symmetries are discussed, in particular their application to the construction of binary decision diagrams and the implementation of Boolean functions. 1.

### Citations

876 | Symbolic Boolean manipulation with ordered binary-decision diagrams
- Bryant
- 1992
(Show Context)
Citation Context ...th the use of Karnaugh-maps. 5. APPLICATIONS 5.1. BDD Minimization The use of symmetries to minimize Binary Decision Diagram (BDD) or related representations is well-documented [6], [14], [15], [16], =-=[17]-=-. Much research has demonstrated that a function’s symmetry properties may reduce the size of the BDD or related data structure such as Functional Decision Diagrams (FDDs) [5], [15], [18], [19]. In pa... |

361 |
Binary decision diagrams
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Citation Context ...re is the output vector for and so on. The relationship between , , , and to , , , and is as follows [1]: 2.4. BDDs Binary Decision Diagrams (BDDs) were first introduced by Lee [9] and later by Akers =-=[10]-=-. A BDD is defined as [11] a binary directed acyclic graph with two leaves TRUE and FALSE, in which each non-leaf node is labeled with a variable and has two out-edges, one pointing to the subgraph th... |

233 | On the complexity of VLSI implementations and graph representations of Boolean functions with applications to integer multiplication
- Bryant
- 1991
(Show Context)
Citation Context ...rly with the use of Karnaugh-maps. 5. APPLICATIONS 5.1. BDD Minimization The use of symmetries to minimize Binary Decision Diagram (BDD) or related representations is well-documented [6], [14], [15], =-=[16]-=-, [17]. Much research has demonstrated that a function’s symmetry properties may reduce the size of the BDD or related data structure such as Functional Decision Diagrams (FDDs) [5], [15], [18], [19].... |

55 |
Representation of switching circuits by binary decision diagrams
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- 1959
(Show Context)
Citation Context ...section as follows: where is the output vector for and so on. The relationship between , , , and to , , , and is as follows [1]: 2.4. BDDs Binary Decision Diagrams (BDDs) were first introduced by Lee =-=[9]-=- and later by Akers [10]. A BDD is defined as [11] a binary directed acyclic graph with two leaves TRUE and FALSE, in which each non-leaf node is labeled with a variable and has two out-edges, one poi... |

54 | Symmetry detection and dynamic variable ordering of decision diagrams
- Panda, Somenzi, et al.
- 1994
(Show Context)
Citation Context ... symmetry properties are commonly used in synthesis of digital circuits [1], [2], [3], [4], particularly in the reduction of the size of Binary Decision Diagram (BDD) representation of functions [5], =-=[6]-=-. Various literature on partial and total symmetries exists (see section 2.2). However, most of the documented symmetry properties depend on the identification of two identifical subfunctions within a... |

30 | Using if-then-else DAGs for multi-level logic minimization
- Karplus
- 1982
(Show Context)
Citation Context ...r and so on. The relationship between , , , and to , , , and is as follows [1]: 2.4. BDDs Binary Decision Diagrams (BDDs) were first introduced by Lee [9] and later by Akers [10]. A BDD is defined as =-=[11]-=- a binary directed acyclic graph with two leaves TRUE and FALSE, in which each non-leaf node is labeled with a variable and has two out-edges, one pointing to the subgraph that is evaluated if the nod... |

29 |
Detection of symmetry of boolean functions represented as robdds
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- 1993
(Show Context)
Citation Context ...e various types of antisymmetries and their definitions. Antisymmetry Definition Table 1. Definitions and notation for the antisymmetries. 4. CONDITIONS AND TESTS FOR THE ANTISYMMETRIES [3], [6], and =-=[12]-=- each present methods of (anti)symmetry detection based on BDDs. In this section we present both conditions and tests for the antisymmetries based on the function’s spectral coefficients. Until recent... |

21 | Efficient Calculation of Spectral Coefficients and Their Applications
- Thornton, Nair
- 1995
(Show Context)
Citation Context ...s were considered too expensive to compute and sosthis technique was not popular. However, Thornton et. al. have presented methods for efficient calculation of the spectral coefficients based on BDDs =-=[13]-=-, thus making spectral techniques feasible for many practical functions. Based on the definitions of the various antisymmetries we recall that can be defined as , or, since the effect of negating a fu... |

20 |
BDD minimization using symmetries
- Scholl, Möller, et al.
- 1999
(Show Context)
Citation Context ...ticularly with the use of Karnaugh-maps. 5. APPLICATIONS 5.1. BDD Minimization The use of symmetries to minimize Binary Decision Diagram (BDD) or related representations is well-documented [6], [14], =-=[15]-=-, [16], [17]. Much research has demonstrated that a function’s symmetry properties may reduce the size of the BDD or related data structure such as Functional Decision Diagrams (FDDs) [5], [15], [18],... |

18 | Multilevel logic synthesis of symmetric switching functions - Kim, Dietmeyer - 1991 |

18 |
Generalized Reed–Muller forms as a tool to detect symmetries
- Tsai, Marek-Sadowaska
- 1996
(Show Context)
Citation Context ... symmetries exist in most Boolean functions, particularly those used in practical applications. Both total and partial symmetry properties are commonly used in synthesis of digital circuits [1], [2], =-=[3]-=-, [4], particularly in the reduction of the size of Binary Decision Diagram (BDD) representation of functions [5], [6]. Various literature on partial and total symmetries exists (see section 2.2). How... |

8 |
Overview of decision diagrams
- Drechsler, Becker
- 1997
(Show Context)
Citation Context ...s, particularly with the use of Karnaugh-maps. 5. APPLICATIONS 5.1. BDD Minimization The use of symmetries to minimize Binary Decision Diagram (BDD) or related representations is well-documented [6], =-=[14]-=-, [15], [16], [17]. Much research has demonstrated that a function’s symmetry properties may reduce the size of the BDD or related data structure such as Functional Decision Diagrams (FDDs) [5], [15],... |

7 | Sympathy: Fast Exact Minimization of Fixed Polarity Reed-Muller Expressions for Symmetric Functions
- Drechsler, Becker
- 1995
(Show Context)
Citation Context ... [16], [17]. Much research has demonstrated that a function’s symmetry properties may reduce the size of the BDD or related data structure such as Functional Decision Diagrams (FDDs) [5], [15], [18], =-=[19]-=-. In particular, Scholl et. al. present a method of BDD minimization based on symmetries [15]. This method is based on heuristics which identify partial symmetries within a function. It is our hypothe... |

6 | Minimizing ROBDD Sizes of Incompletely Specified Boolean Functions by Exploiting Strong Symmetries
- Scholl, Melchior, et al.
- 1997
(Show Context)
Citation Context ... [15], [16], [17]. Much research has demonstrated that a function’s symmetry properties may reduce the size of the BDD or related data structure such as Functional Decision Diagrams (FDDs) [5], [15], =-=[18]-=-, [19]. In particular, Scholl et. al. present a method of BDD minimization based on symmetries [15]. This method is based on heuristics which identify partial symmetries within a function. It is our h... |

3 | Least Upper Bounds for the Size of OBDDs Using Symmetry Properties
- Heinrich-Litan, Molitor
(Show Context)
Citation Context ...rtial symmetry properties are commonly used in synthesis of digital circuits [1], [2], [3], [4], particularly in the reduction of the size of Binary Decision Diagram (BDD) representation of functions =-=[5]-=-, [6]. Various literature on partial and total symmetries exists (see section 2.2). However, most of the documented symmetry properties depend on the identification of two identifical subfunctions wit... |

2 |
ªLeast Upper Bounds on the Sizes of Symmetric Variable Order Based OBDDs,º
- Litan, Molitor, et al.
- 1996
(Show Context)
Citation Context ...t to a set if remains unchanged for all permutations of the variables in . If then we say that the function is totally symmetric, otherwise we say that it is partially symmetric over the variables in =-=[8]-=-. A symmetry of degree two is a partial symmetry in which the two subfunctions that are identical are independent of two of the function’svariables. Our antisymmetries are based on Hurst et. al’s. def... |