A universal interconnection network implements arbitrary interconnections among n terminals. This paper considers a problem to realize such a network using contact switches. When n = 2, it can be implemented with a si...
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A universal interconnection network implements arbitrary interconnections among n terminals. This paper considers a problem to realize such a network using contact switches. When n = 2, it can be implemented with a single switch. The number of different connections among n terminals is given by the Bell number B(n). The Bell number shows the total number of methods to partition n distinct elements. For n = 2, 3, 4, 5 and 6, the corresponding Bell numbers are 2, 5, 15, 52, and 203, respectively. This paper shows a method to realize an n terminal universal interconnection network with 3/8(n(2)-1) contact switches when n = 2m+ 1 = 5, and n/8(3n + 2) contact switches, when n = 2m >= 6. Also, it shows that a lower bound on the number of contact switches to realize an n-terminal universal interconnection network is [log(2) B(n)], where B(n) is the Bell number.
We show that the system of elementary conjunctions omega(n,2)k = K-0, ... , K-2(k)-1 such that each conjunction depends essentially on n variables and corresponds to some codeword of a linear (n, k)-code can be implem...
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We show that the system of elementary conjunctions omega(n,2)k = K-0, ... , K-2(k)-1 such that each conjunction depends essentially on n variables and corresponds to some codeword of a linear (n, k)-code can be implemented by a separating contact circuit of complexity at most 2(k+1 )+ 4k(n - k) - 2. We also show that if a contact (1, 2(k))-terminal network is separating and implements the system of elementary conjunctions omega(k)(n,2), then the number of contacts in it is at least 2(k+1 )- 2.
作者：
Hodes, LouisDepartment of Health
Education and Welfare Division of Computer Research and Technology National Institutes of Health Public Health Service United States
The logical complexity of some geometrical properties such as convexity and congruence in the plane is considered. These properties are characterized by the length of formulas necessary to express them. The main resul...
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A universal interconnection network implements arbitrary interconnections among n terminals. This paper considers a problem to realize such a network using contact switches. When n = 2, it can be implemented with a si...
详细信息
ISBN:
(纸本)9781728154060
A universal interconnection network implements arbitrary interconnections among n terminals. This paper considers a problem to realize such a network using contact switches. When n = 2, it can be implemented with a single switch. The number of different connections among n terminals is given by the Bell number B(n). The Bell number shows the total number of methods to partition n distinct elements. For n = 2, 3, 4, 5 and 6, the corresponding Bell numbers are 2, 5, 15, 52, and 203, respectively. This paper shows a method to realize an n terminal universal interconnection network with 3/8 (n(2)-1) contact switches when n = 2m + 1 >= 5, and n/8 (3n + 2) contact switches, when n = 2m >= 6. Also, it shows a lower bound on the number of contact switches to realize an n-terminal universal interconnection network.
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