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  • Boolean algebra  (1)
  • Primary 08A25, 02C05  (1)
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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Aequationes mathematicae 25 (1982), S. 274-288 
    ISSN: 1420-8903
    Schlagwort(e): Primary 08A25, 02C05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract LetA be a finite set,n≥1 andD⊆A n. We say thatf :D →A is a functionally complete partial operation of size |D| if eachf*:A n →A agreeing withf onD is functionally complete. Such an operation of sized represents thus a family of $$|A|^{(|A|^n - d)} $$ functionally complete operations. We investigate the least possible size of functionally complete partial groupoids. Such groupoids not defined on a row or column have size either |A|+1 or |A|+2 or are of size at least 2|A|−2. We prove that |A|+1 is the least size of such a groupoid and completely determine those of size |A|+1. As one might expect, these groupoids are very special. This study shows how surprisingly little information is needed to ensure that a groupoid is functionally complete and, at the same time, gives a description of large classes of functionally complete groupoids.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 2
    Digitale Medien
    Digitale Medien
    Springer
    International journal of parallel programming 6 (1977), S. 151-163 
    ISSN: 1573-7640
    Schlagwort(e): Switching theory ; logic design ; combinational circuits ; Boolean algebra ; circuit simplication
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Abstract A new notation for a NAND operator is proposed, based on the prefix Polish notation following the style of Lukasiewicz. There is a direct one-to-one correspondence between the operators in the resulting system and gates in a circuit realization if identical subfunctions are recognized. An axiom set for the Boolean algebra based on this operator is given, and the axiomatic derivation of the algebra is demonstrated. A number of results concerning circuit manipulation, redundant sets of gate inputs, and necessary and sufficient conditions for the relocation of certain gate inputs are presented, and their use demonstrated by a number of examples.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
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