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Determination of the irredundant forms of a Boolean function using Walsh-Hadamard analysis and dyadic groups Author s : Philipp W. Add to cart.

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Invalid site public key. Thank you Your recommendation has been sent to your librarian. Author s : Philipp W. Transform methods and dyadic groups have been used for the classification of Boolean functions as well as for prime implicant determination. In a recent paper a prime implicant extraction method, based on Walsh-Hadamard transform methods, was presented.

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It processes the true minterms of the function separately, one at a time. In this paper this transform method is applied to the covering problem.

Taking the prime implicants as binary variables a slight modification of the prime-implicant extraction method allows one to identify all complete covers by inspecting the elements of an inverse transform. Redundant forms can be detected and rejected easily. Another method for the determination of all irredundant covers classifies the 2 m elements of the dyadic group of element length m as incomplete, redundant or irredundant covers, m beingthe number of prime implicants.

A version for hand-worked problems is given, as well as a computer-oriented version. Inspec keywords: Boolean functions ; transforms Other keywords: binary variables ; Walsh Hadamard analysis ; dyadic groups ; Boolean function ; prime implicant extraction method Subjects: Formal logic.

References 1 N. Ahmed , K. Besslich , K. Neumann , R. NTZ Commun.

On the Walsh-Hadamard transform and prime implicant extraction. IEEE Trans.

Weighting Method for the determination of the irredundant set of prime implicants. Dunham , R. The problem of simplifying logical expressions. The application of the Rademacher-Walsh transform to Boolean function classification and threshold logic syntheses. Irredundant disjunctive and conjunctive forms of a Boolean function.

IBM J. On the classification of Boolean functions.

IRE Trans. The application of Chow parameters and Rademacher-Walsh matrices in the synthesis of binary functions.

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Lechner , A. An algorithm for the automatic approximate minimization of Boolean functions. Weighting method for the determination of the irredundant set of prime implicants. Report, Giloi , H. Generation of prime implicants from subfunctions and a unifying approach to the covering problem. Zander , W.