## Parity Function Detection and Realization Using a Small Set of Spectral Coefficients (1995)

Venue: | IEEE/ACM INTERNATIONAL WORKSHOP ON LOGIC SYNTHESIS (IWLS |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Thornton95parityfunction,

author = {M. A. Thornton and V. S. S. Nair},

title = {Parity Function Detection and Realization Using a Small Set of Spectral Coefficients},

booktitle = { IEEE/ACM INTERNATIONAL WORKSHOP ON LOGIC SYNTHESIS (IWLS},

year = {1995},

pages = {8--39},

publisher = {}

}

### OpenURL

### Abstract

A technique to detect and realize a parity logic function using a linear number of spectral coefficients is presented. Recent advances in computation methods for the spectra of a Boolean function have resulted in the determination of a single coefficient very efficiently. The use of a small set of spectral coefficients offers low cost and attractive alternatives to more traditional digital logic design and analysis techniques when coupled with the use of the new spectral computation approach. The detection and realization of the class of parity functions is an important problem since it generally requires the computation of 2 n Walsh coefficients when spectral methods are used, or, extensive symbolic algebraic manipulation when other methods are used. The method presented in this paper only requires the computation of n + 2 Walsh coefficients and n + 1 non-Walsh coefficients to detect and realize a parity function.

### Citations

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Citation Context ...nt input. However, the fact that a particular coefficient is computed to be 0 does not necessarily imply that the corresponding x i is redundant. This property is formally proven in the work given in =-=[10]-=-. The fact that degenerate functions will always have at least one zero-valued Chow parameter is used in the method we develop here, thus, in the remainder of this paper we assume the Chow parameters ... |

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Citation Context ...function is defined as a vector of integer values obtained through the linear mapping of a specific transformation matrix. Common transformation matrices include the Reed-Muller transformation matrix =-=[2]-=-, or the Walsh family of matrices such as the Rademacher-Walsh or Hadamard [3]. As developed in [4], each row of the transformation matrix may be considered to be the output vector of a logic function... |

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24 | Efficient Calculation of Spectral Coefficient and Their Application
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Citation Context ...circuit optimizers require a structural input and provide an output that is also in a netlist form. Recently, some efficient spectral computation methods have been proposed that use BDDs as input [1] =-=[6]-=- [7] [8]. However, if the circuit is in the form of a netlist initially, it may be more work to obtain a suitable variable ordering and then build a BDD representation than it would be to compute the ... |

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Citation Context ...optimizers require a structural input and provide an output that is also in a netlist form. Recently, some efficient spectral computation methods have been proposed that use BDDs as input [1] [6] [7] =-=[8]-=-. However, if the circuit is in the form of a netlist initially, it may be more work to obtain a suitable variable ordering and then build a BDD representation than it would be to compute the spectral... |

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Citation Context ... transformation matrix. Common transformation matrices include the Reed-Muller transformation matrix [2], or the Walsh family of matrices such as the Rademacher-Walsh or Hadamard [3]. As developed in =-=[4]-=-, each row of the transformation matrix may be considered to be the output vector of a logic function, and thus the transformation matrices may be viewed as being composed of a collection of logic fun... |

3 | Efficient Spectral Coefficient Calculation Using Circuit Output Probabilities
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Citation Context ... advent of an efficient method for the computation of a single spectral coefficient of a Boolean function comes a renewed interest in the use of these quantities for circuit design and analysis tasks =-=[1]-=-. In particular, methods that use a small subset of spectral coefficients are especially attractive since the computational efficiency provided by the new calculation technique is augmented by reducin... |

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Citation Context ...onential number of BDD vertices versus a much smaller netlist. For these classes of circuits, the use of an efficient spectral computation technique using a structural input such as that described in =-=[9]-=- is clearly advantageous. The remainder of this paper is organized as follows. Section 2 contains a brief discussion of the notation and definitions used in this development. Section 3 contains the ma... |