Tabular techniques for generating Kronecker expansions

Almaini, A. E. A.; McKenzie, L.

doi:10.1049/ip-cdt:19960564

Cited by 24 publications

(13 citation statements)

References 6 publications

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“…Assuming that conversion is from P l to P m ; (p k ) l and (p k ) m are the k-th bit of the two polarities; (x n-1 ,x n-2 ,···,x 0 ) is one term in n-variable MPRM function. Summing up the conversion algorithm [9] and converting all the negatively biased variable into positively biased variable, then the algorithm for the conversion from polarity l to polarity m can be listed as follows:…”

Section: B Minimization Scheme Of Mprm Expansionmentioning

confidence: 99%

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Low-Power Synthesis for MPRM Circuit Based on Exhaustive Algorithm

Wang

2010

2010 International Conference on Multimedia Technology

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In this paper, a low-power synthesis algorithm is proposed. Based on polarity conversion technique, the minimal Mixed-polarity Reed-Muller (MPRM) expansions are searched with exhaustive algorithm. Then the corresponding MPRM circuits are decomposed in dynamic logic and the optimal power is gotten. MCNC benchmark circuits are tested and the results are performed with the Fixed-Polarity Reed-Muller (FPRM) circuits of the minimal power. It shows that the expansion and power are smaller in MPRM circuits, and the decrease rates are 47.8% and 29.6%, respectively.

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Section: B Minimization Scheme Of Mprm Expansionmentioning

confidence: 99%

“…Tabular technique [9] is applied to conversion to search the minimal expansion. Assuming that conversion is from P l to P m ; (p k ) l and (p k ) m are the k-th bit of the two polarities; (x n-1 ,x n-2 ,···,x 0 ) is one term in n-variable MPRM function.…”

Section: B Minimization Scheme Of Mprm Expansionmentioning

confidence: 99%

Low-Power Synthesis for MPRM Circuit Based on Exhaustive Algorithm

Wang

2010

2010 International Conference on Multimedia Technology

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“…In fixed polarity Reed-Muller (FPRM) expressions, each variable can only be either true or complemented, but not both. One obvious advantage of FPRM forms over SOP or mixed polarity Reed-Muller forms is the absence of redundant variables [8] although there are other complex expansions available [9][10][11][12]. Moreover, applications of FPRM forms to Boolean matching [13], symmetry detection [14], and functions classification [15] have been reported.…”

Section: Introductionmentioning

confidence: 99%

Exact minimisation of large multiple output FPRM functions

Wang

Almaini

2002

IEE Proc., Comput. Digit. Tech.

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The properties of the polarity for sum-of-products (SOP) expressions of Boolean functions are formally investigated. A transform matrix S is developed to convert SOP expressions from one polarity to another polarity. It is shown that the effect of SOP polarity is to reorder the onset minterms of a Boolean function. Furthermore, the transform matrix P for fixed polarity Reed-Muller (FPRM) expressions for the conversion between two different polarities, based on the properties of SOP polarity, is achieved. Comparison of these two matrices shows that the Reed-Muller transform matrix P has a much more complex structure. Additionally, the best polarity of FPRM forms with the least onset terms corresponds with the polarity of SOP forms with the best 'order' of the onset minterms. Applying these algebraic properties of the transform matrix P, a fast algorithm is presented to obtain the best polarity of FPRM expressions for large multiple output Boolean functions. The computation time is independent of the number of outputs. The developed program is tested on common personal computers and the results for benchmark examples of up to 25 inputs and 29 outputs are presented.

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“…The tabular technique for calculation of FPRM expressions proposed in [19] is an improvement of approaches presented in [2,1]. This TT starts from a table of minterms for a given switching function .…”

Section: Tabular Technique For Fprmgfementioning

confidence: 99%

“…The term Tabular Techniques (TTs) usually refers to methods derived for minterm representations [1,2,19]. TTs exploit linearity of Reed-Muller expressions, which permits to determine the value of a coefficient in FPRM expressions for as the EXOR sum of the contributions of each true minterm in to [19].…”

Section: Introductionmentioning

confidence: 99%

Efficient calculation of fixed-polarity polynomial expressions for multiple-valued logic functions

Janković

Stanković

Drechsler

Proceedings 32nd IEEE International Symposium on Multiple- Valued Logic

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This paper presents a tabular technique for calculation of fixed-polarity polynomial expressions for MV functions. The technique is derived from a generalization of the corresponding methods for Fixed-Polarity Reed-Muller (FPRM) expressions for switching functions. All useful features of tabular techniques for FPRMs, as for example, simplicity of involved operations and high possibilities for parallelization of the calculation procedure, are preserved. The method can be extended to the calculation of coefficients in Kronecker expressions for MV functions.

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Tabular techniques for generating Kronecker expansions

Cited by 24 publications

References 6 publications

Low-Power Synthesis for MPRM Circuit Based on Exhaustive Algorithm

Low-Power Synthesis for MPRM Circuit Based on Exhaustive Algorithm

Exact minimisation of large multiple output FPRM functions

Efficient calculation of fixed-polarity polynomial expressions for multiple-valued logic functions

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