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By David C. Rine

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Extra resources for Computer Science and Multiple-Valued Logic. Theory and Applications

Example text

This 4-stable device (two Eccles-Jordan circuits) considered as a unit is a non-symmetric circuit whose expense is 100% over that of the 2-stable device (one Eccles-Jordan circuit), with slight additional expense to obtain the noted representations. Now it is well known from information theory that n = 3 states give more entropy per state cost than does either n = 2 or n = 4 states, based on the assumption that the cost is linearly proportional to the number of states. The above example suggests strongly the possibility of designing a non-symmetric, 3 transistor device, whose cost is close to 50% over that of the Eccles-Jordan bi-stable circuit.

102-114). [9] G. Gratzer, Lattice Theory, First Concepts and Distributive Lattices, (Freeman, San Francisco, 1971). [10] S. Su and A. Sarris, The relationship between multivalued switching algebra and Boolean algebra under different definitions of complement, IEEE Trans. Computers, C-21 (1972) 479-485. chain based lattices* g. epstein a. horn In recent years several weakenings of Post algebras have been studied. Among these have been Po-lattices by T. Traczyk, Stone lattice of order n by T. Katrinak and A.

Is a Post function of m variables X i , . . , eim )G,(*i) • • • Gu (xm). Proof. There are nm terms of the form Ciixx)Ch{x2) - • • CIm(jcm), and these are called the fundaments of the m variables. It follows from Axiom 1 that (1) distinct fundamentals are disjoint, and (2) the supremum of all the fundaments is u; in fact, the infimum of two distinct fundaments must include an infimum of the form Ci(Xj)Ck(Xj) = 0, where iV k for some /, and V Cii(x1) • • • CIm(jcm) = A ( V QOc,)) = A (u) = u.

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