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Orthogonal Block Building Using Ordered Lists of Ternary Vectors
 Freiberg University of Mining and Technology
, 2000
"... . In this paper we investigate the possibility of faster calculation of operations on Boolean functions. We use the representation of a function as an ordered list of ternary or Boolean vectors and propose a faster algorithm that is based on ordering of vectors. We sort the vectors in lists using t ..."
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. In this paper we investigate the possibility of faster calculation of operations on Boolean functions. We use the representation of a function as an ordered list of ternary or Boolean vectors and propose a faster algorithm that is based on ordering of vectors. We sort the vectors in lists using the number of ones and strokes to create classes and subclasses. This model is used to speed up the minimization of orthogonal vector lists, an algorithm known as block building. Our algorithm is compared with three other algorithms, and finally it is shown by means of experimental results that our algorithm with ordering of vectors require fewer comparisons and can find more pairs of vectors, which can build a block. 1. Introduction Recently, two fundamental approaches are used for representation of Boolean functions. In contrast to decision diagrams (DD's) representation, in this paper we will focus on the data structures List of Boolean Vectors (BVL) and List of Ternary Vectors (TVL) [1...
Ch.: Several Approaches to Parallel Computing in the Boolean Domain. in
 D.: 2010 1st International Conference on Parallel, Distributed and Grid Computing (PDGC 2010), October 28  30, 2010, Jaypee University of Information Technology Waknaghat
, 2010
"... Abstract—Each additional variable doubles the number of function values of a Boolean function. This exponential increase is known as combinational explosion and limits strongly the solvable problems for a given computer. In order to solve larger Boolean problems, it is necessary to exploit each conc ..."
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Abstract—Each additional variable doubles the number of function values of a Boolean function. This exponential increase is known as combinational explosion and limits strongly the solvable problems for a given computer. In order to solve larger Boolean problems, it is necessary to exploit each concept that reduces the required efforts. The parallel consideration of all Boolean variables that are assigned to a machine word of the computer, the mapping of an exponential number of Boolean vectors to a single ternary vector, and the distribution of the calculations to several Boolean spaces are some approaches which were realized in the software package XBOOLE. An important further approach is the segmentation of the Boolean tasks and their parallel computation using several connected computers as well as the available processor cores of these computers. In this paper we explore alternative approaches to parallel computations of Boolean problems. Experimental results document the achieved benefits. Index Terms—Parallel computing, Boolean function; message passing interface; XBOOLE. I.
Orthogonal Block Change Block Building
, 2003
"... In this paper we present an improved algorithm for efficient minimization of the number of vectors in lists representing Boolean functions using an ordered data structure OTVL and simulated annealing algorithm to permit with a certain probability performing of some special block changes. New algorit ..."
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In this paper we present an improved algorithm for efficient minimization of the number of vectors in lists representing Boolean functions using an ordered data structure OTVL and simulated annealing algorithm to permit with a certain probability performing of some special block changes. New algorithm requires fewer comparisons to find a new block building possibility than the XBOOLE algorithm.
Orthogonal Block Change Block Building Using Ordered Lists of Ternary Vectors
 Freiberg University of Mining and Technology
, 2002
"... In this paper we investigate the possibility of efficient minimization of number of vectors in lists representing Boolean functions. We use the representation of a function as an ordered list of ternary or Boolean vectors and propose a faster algorithm that is based on ordering of vectors. We sort t ..."
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In this paper we investigate the possibility of efficient minimization of number of vectors in lists representing Boolean functions. We use the representation of a function as an ordered list of ternary or Boolean vectors and propose a faster algorithm that is based on ordering of vectors. We sort the vectors in lists using the number of ones and dashes to create classes and subclasses. This model is used to speed up the optimization of orthogonal vector lists, an algorithm known as block change & block building. Unlike the algorithm used in XBOOLE system this algorithm uses additional knowledge from the ordered model and changes only blocks, that lead to new possibilities of block building. Our new algorithm is compared with algorithm, used in XBOOLE system, and finally it is shown by means of experimental results that our algorithm with ordering of vectors requires fewer comparisons to find a new block building possibility.
CALCULATION OF SET OPERATIONS USING ORDERED LISTS OF TERNARY VECTORS
"... Abstract. The synthesis, the test, and the verification of complex digital circuits need efficient set operations on Boolean functions. This paper presents faster algorithms for calculation of set operations: difference, union, symmetrical difference, complement of symmetrical difference and complem ..."
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Abstract. The synthesis, the test, and the verification of complex digital circuits need efficient set operations on Boolean functions. This paper presents faster algorithms for calculation of set operations: difference, union, symmetrical difference, complement of symmetrical difference and complement. The suggested data structure to represent a Boolean function is the Ordered List of Ternary Vectors (OTVL). The ordering is organized into classes and subclasses relating to the numbers of ones and strokes. Experimental results show that OTVL needs in average only 45 % of the number of necessary comparisons of pairs of ternary vectors compared with employing of Ternary Vector List.