Showing papers on "Logical matrix published in 1979"
TL;DR: A parallel algorithm which uses n=2 processors to find the connected components of an undirected graph with n vertices in time in time O(n), which can be used to finding the transitive closure of a symmetric Boolean matrix.
Abstract: We present a parallel algorithm which uses n2 processors to find the connected components of an undirected graph with n vertices in time O(log2n). An O(log2n) time bound also can be achieved using only n⌈n/⌈log2n⌉⌉ processors. The algorithm can be used to find the transitive closure of a symmetric Boolean matrix. We assume that the processors have access to a common memory. Simultaneous access to the same location is permitted for fetch instructions but not for store instructions.
266 citations
TL;DR: It is shown that Swamy's approach to generate generalized Reed–Muller canonic expansion is in error and a different algorithm is presented which uses a single Boolean matrix and successive modifications in function vector to generate all the solutions sequentially.
Abstract: It is shown that Swamy's [1] approach to generate generalized Reed–Muller canonic expansion is in error. A different algorithm is presented which uses a single Boolean matrix and successive modifications in function vector to generate all the solutions sequentially.
40 citations
25 citations
Patent•
06 Apr 1979
TL;DR: In this article, a binary matrix of elements and sub-sets is expressed by the binary matrix, in which the relationships between the elements are indicated at letter X and the elements themselves were indicated at letters A to N, so that it may be fed from a card input device or a key board.
Abstract: PURPOSE:To efficiently accomplish the selection of sub-sets and the display of construction numbering the matrix, which is composed of elements and sub-sets relating thereto, so that the designated sub-sets (or transverse sub-sets) may be displayed in changed brightness CONSTITUTION:The construction of the graph to be analyzed is expressed by the binary matrix, in which the relationships between the elements are indicated at letter X and the elements themselves are indicated at letters A to N, so that it may be fed from a card input device 2 or a key board 4 In accordance with this input, a centralized operational device 1 is designated in algorithm so that the sub-sets mutually coupled at a ratio higher than a coupling value to form a matrix of elements and sub-sets, which is displayed in a display device 3 and fed to a printer 6 In accordance with the numbers of the matrix, the transverse sub-sets are designated and displayed in a display plate 7 in a display plate 7 in a different brightness from that of the non-designated sub-sets The desired sub-sets are effectively selected and displayed from the multiple sub-sets to satisfactorily analyze the construction On the other hand, the matrix of the elements and the sub-sets is stored in a memory so that the displayed construction can be easily corrected
3 citations
TL;DR: It is shown that an arbitrary matrix form with only one nonterminal symbol does not generate the family of context-free languages if it contains a matrix with at least two productions.
Abstract: This paper deals with the concepts of a matrix form and strict interpretation. By a matrix form we mean a context-free matrix grammar. Via an interpretation mechanism it generates a family of structurally related grammars and these generate a family of languages. We study here the properties of matrix forms as generators for the families of regular, linear and context-free languages. It is for instance shown that an arbitrary matrix form with only one nonterminal symbol does not generate the family of context-free languages if it contains a matrix with at least two productions.
1 citations
TL;DR: Fast parallel matrix multiplication algorithms in SIMD and MIMD modes are described for implementation in a parallel-binary matrix processing system with facilities for bit-wise parallel Boolean operation and power-of-two shifts on Boolean matrices.
Abstract: : Fast parallel matrix multiplication algorithms in SIMD (Single-Instruction-Multiple-Data) and MIMD (MUltiple-Instruction-Multiple-data) modes are described for implementation in a parallel-binary matrix processing system with facilities for bit-wise parallel Boolean operation and power-of-two shifts on Boolean matrices. A comparative study of these algorithms is made on the basis of their relative time-complexities, when conventional binary and prime-modulus arithmetic are used for forming the matrix product. (Author)
1 citations
01 Jan 1979
TL;DR: A sufficient criterion for the finite Church-Rosser property is given, and it is shown how this property can be proved by using a simple set oriented Boolean matrix calculus.
Abstract: Algorithms consisting of repetitive change to a given graph are described in a manner adapted to graph theoretic applications. Easily provable attributes are defined, a sufficient criterion for the finite Church-Rosser property is given, and it is shown how this property can be proved by using a simple set oriented Boolean matrix calculus. As an application a new and efficient algorithm for finding the interval graph of a flow graph is derived.