## Exploring multi-valued minimization using binary methods (2003)

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Venue: | in International Workshop on Logic and Synthesis |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Mishchenko03exploringmulti-valued,

author = {Alan Mishchenko},

title = {Exploring multi-valued minimization using binary methods},

booktitle = {in International Workshop on Logic and Synthesis},

year = {2003}

}

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### Abstract

A transformation of multi-valued input binary-output functions, called co-singleton transform (CST), was introduced in [11] to reduce algebraic multi-valued (MV) operations to binary. In this paper, we explore its potential for a number of problems related to MV SOP minimization, such as computing ISOPs, the set of all primes, and the set of all essential primes. Experimental results show that in some cases these problems can be solved more efficiently than by the traditional MV SOP minimization approaches represented by ESPRESSO-MV, but that generally there is no clear method-of-choice. 1

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3134 | Graph-based algorithms for boolean function manipulation
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Citation Context ...and, in particular, concepts of literal, cube, prime, essential primes. (2) Multi-valued SOP minimization [23] and extension of the above concepts for the MV case. (3) Binary Decision Diagrams (BDDs) =-=[4]-=-, in particular, concepts of cofactoring, ITE operator, the generic structure of a BDD traversal procedure. (4) Zero-suppressed Binary Decision Diagrams (ZDDs) [16] and, in particular, ZDD representat... |

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Logic Minimization Algorithms for VLSI Synthesis
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Citation Context ...y ESPRESSO-MV, but that generally there is no clear method-of-choice. 1 Introduction Several approaches have been proposed to minimize an SOP representation of binary multi-output logic functions [10]=-=[2]-=-[8] and to solve related problems, such as the computation of ISOPs [20][17][5], the set of all primes [20][5], and the set of essential primes [25][5]. The problem of SOP minimization has been solved... |

152 |
Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems
- Minato
- 1993
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Citation Context ... (3) Binary Decision Diagrams (BDDs) [4], in particular, concepts of cofactoring, ITE operator, the generic structure of a BDD traversal procedure. (4) Zero-suppressed Binary Decision Diagrams (ZDDs) =-=[16]-=- and, in particular, ZDD representation of combinatorial sets and cube covers. (5) MV functions and relations, as defined in [19].sWe refer to completely specified functions as CSFs and incompletely s... |

108 |
The decomposition and factorization of Boolean expressions
- Brayton, McMullen
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Citation Context ...transform (CST) [11], can be used to transform a binary solution into a solution of the original MV problem. The approach [11] was applied successfully to algebraic extraction of logic in MV networks =-=[3]-=-[22], resulting in comparable quality and noticeable reduction in runtime, compared to a purely MV algebraic approach [9]. Experiments were done only in applications where algebraic operations were pe... |

72 | Implicit and incremental computation of primes and essential primes of boolean functions
- Coudert, Madre
- 1992
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Citation Context ...ction Several approaches have been proposed to minimize an SOP representation of binary multi-output logic functions [10][2][8] and to solve related problems, such as the computation of ISOPs [20][17]=-=[5]-=-, the set of all primes [20][5], and the set of essential primes [25][5]. The problem of SOP minimization has been solved successfully for multi-valued-input binary-output functions (MV functions, for... |

55 | MINI: A Heuristic Approach for Logic Minimization
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- 1974
(Show Context)
Citation Context ...ed by ESPRESSO-MV, but that generally there is no clear method-of-choice. 1 Introduction Several approaches have been proposed to minimize an SOP representation of binary multi-output logic functions =-=[10]-=-[2][8] and to solve related problems, such as the computation of ISOPs [20][17][5], the set of all primes [20][5], and the set of essential primes [25][5]. The problem of SOP minimization has been sol... |

32 | Espresso-Signature: A new Exact Minimizer for Logic Functions - McGeer, Sanghavi, et al. - 1993 |

25 | Simplification of nondeterministic multi-valued networks
- Mishchenko, Brayton
(Show Context)
Citation Context ...aversal procedure. (4) Zero-suppressed Binary Decision Diagrams (ZDDs) [16] and, in particular, ZDD representation of combinatorial sets and cube covers. (5) MV functions and relations, as defined in =-=[19]-=-.sWe refer to completely specified functions as CSFs and incompletely specified functions as ISFs. Unless specifically stated, a CSF or ISF has multi-valued-inputs and a binary output. An ISF can be r... |

20 |
Fast generation of irredundant sum-of-products forms from binary decision diagrams
- Minato
(Show Context)
Citation Context ...roduction Several approaches have been proposed to minimize an SOP representation of binary multi-output logic functions [10][2][8] and to solve related problems, such as the computation of ISOPs [20]=-=[17]-=-[5], the set of all primes [20][5], and the set of essential primes [25][5]. The problem of SOP minimization has been solved successfully for multi-valued-input binary-output functions (MV functions, ... |

17 |
Two-level logic minimization: an overview. Integration
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Citation Context ...SPRESSO-MV, but that generally there is no clear method-of-choice. 1 Introduction Several approaches have been proposed to minimize an SOP representation of binary multi-output logic functions [10][2]=-=[8]-=- and to solve related problems, such as the computation of ISOPs [20][17][5], the set of all primes [20][5], and the set of essential primes [25][5]. The problem of SOP minimization has been solved su... |

13 | Synthesis of Finite State Machines: Functional Optimization - Kam, Villa, et al. - 1997 |

10 |
Recursive Operators for Prime Implicant and Irredundant Normal Form Determination
- Morreale
- 1970
(Show Context)
Citation Context ... Introduction Several approaches have been proposed to minimize an SOP representation of binary multi-output logic functions [10][2][8] and to solve related problems, such as the computation of ISOPs =-=[20]-=-[17][5], the set of all primes [20][5], and the set of essential primes [25][5]. The problem of SOP minimization has been solved successfully for multi-valued-input binary-output functions (MV functio... |

9 | Implicit Prime Cover Computation: An Overview - Coudert, Madre, et al. |

8 |
Semi-algebraic methods for multi-valued logic
- Gao, Brayton
- 2000
(Show Context)
Citation Context ... [11] was applied successfully to algebraic extraction of logic in MV networks [3][22], resulting in comparable quality and noticeable reduction in runtime, compared to a purely MV algebraic approach =-=[9]-=-. Experiments were done only in applications where algebraic operations were performed. In is natural to try to extend this success to apply the CST to Boolean problems, in particular those related to... |

7 |
Symbolic Prime Generation for Multiple-Valued Functions
- Lin, Coudert, et al.
- 1992
(Show Context)
Citation Context ...ions, implicit algorithms to compute a) MV-ISOPs [17], b) the set of all MV-primes, and c) the set of all MV-essential primes. Except for an implicit algorithm to compute the primes of an MV function =-=[13]-=-, no comparable algorithms are known. The paper is organized as follows. Section 2 introduces terminology and notation. Section 3 defines the CST. Sections 4, 5, and 6 discuss algorithms for ISOP, pri... |

6 | Reduced offsets for two-level multi-valued logic minimization - Malik, Brayton, et al. |

5 | Towards a Symbolic Logic Minimization Algorithm - Coudert, Madre - 1993 |

5 |
EXTRA Library of DD procedures
- Mishchenko
(Show Context)
Citation Context ...e 10. Computing essential primes without computing primes. 7 Experimental results The algorithms for ISOP and prime computation were implemented in C using the CUDD package [27] and the EXTRA library =-=[18]-=-. The implementation was tested using a 994GHz 256Mb RAM computer under Windows XP. Table 1 compares several algorithms for ISOP computation. The MV-input binary-output benchmarks were derived from Es... |

4 |
Computer design of multiple-output logical networks
- Bartee
- 1961
(Show Context)
Citation Context ...ach. The number of primes is the same in all the prime computation methods (of course). The subsequent three columns contain the runtime of the CST-based computation, the output-1hot-encoded approach =-=[1]-=-[2][8], and the explicit MV prime computation in Espresso-MV [23]. The 1-hot-encoded representation was only implemented for binary-input functions. Therefore, column “1-hot” is not listed on the righ... |

2 |
Reducing multivalued algebraic operations to binary
- Jiang, Mishchenko, et al.
- 2003
(Show Context)
Citation Context ...artment of EECS UC Berkeley Berkeley, CA 94720 alanmi@eecs.berkeley.edu Abstract A transformation of multi-valued input binary-output functions, called co-singleton transform (CST), was introduced in =-=[11]-=- to reduce algebraic multi-valued (MV) operations to binary. In this paper, we explore its potential for a number of problems related to MV SOP minimization, such as computing ISOPs, the set of all pr... |