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Multilinear Algebra and Chess Endgames
 of No Chance: Combinatorial Games at MRSI
, 1996
"... Abstract. This article has three chief aims: (1) To show the wide utility of multilinear algebraic formalism for highperformance computing. (2) To describe an application of this formalism in the analysis of chess endgames, and results obtained thereby that would have been impossible to compute usi ..."
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Abstract. This article has three chief aims: (1) To show the wide utility of multilinear algebraic formalism for highperformance computing. (2) To describe an application of this formalism in the analysis of chess endgames, and results obtained thereby that would have been impossible to compute using earlier techniques, including a win requiring a record 243 moves. (3) To contribute to the study of the history of chess endgames, by focusing on the work of Friedrich Amelung (in particular his apparently lost analysis of certain sixpiece endgames) and that of Theodor Molien, one of the founders of modern group representation theory and the first person to have systematically numerically analyzed a pawnless endgame. 1.
A note on join and autointersection of nary rational relations
 Proc. Eindhoven FASTAR Days, number 04–40 in TU/e CS TR
, 2004
"... A finitestate machine with n tapes describes a rational (or regular) relation on n strings. It is more expressive than a relational database table with n columns, which can only describe a finite relation. We describe some basic operations on nary rational relations and propose notation for them. ..."
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A finitestate machine with n tapes describes a rational (or regular) relation on n strings. It is more expressive than a relational database table with n columns, which can only describe a finite relation. We describe some basic operations on nary rational relations and propose notation for them. (For generality we give the semiringweighted case in which each tuple has a weight.) Unfortunately, the join operation is problematic: if two rational relations are joined on more than one tape, it can lead to nonrational relations with undecidable properties. We recast join in terms of “autointersection” and illustrate some cases in which difficulties arise. We close with the hope that partial or restricted algorithms may be found that are still powerful enough to have practical use.
Mapping Regular Recursive Algorithms To FineGrained Processor Arrays
, 1994
"... With the continuing growth of VLSI technology, specialpurpose parallel processors have become a promising approach in the quest for high performance. Finegrained processor arrays have become popular as they are suitable for solving problems with a high degree of parallelism, and can be inexpensive ..."
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With the continuing growth of VLSI technology, specialpurpose parallel processors have become a promising approach in the quest for high performance. Finegrained processor arrays have become popular as they are suitable for solving problems with a high degree of parallelism, and can be inexpensively built using custom designs or commercially available field programmable gate arrays (FPGA). Such specialized designs are often required in portable computing and communication systems with realtime constraints, as softwarecontrolled processors often fail to provide the necessary throughput. This thesis addresses many issues in designing such applicationspecific systems built with finegrained processor arrays for regular recursive uniform dependence algorithms. A uniform dependence algorithm consists of a set of indexed computations and a set of uniform dependence vectors which are independent of the indices of computations. Many important applications in signal/image processing, commun...
Periodic Sets of Integers
 Theoretical Computer Science
, 1994
"... Consider the following kinds of sets { the set of all possible distances between two vertices of a directed graph. { any set of integers that is either nite or periodic for all n greater or equal to some n0 (such a set is called ultimately periodic). { a context free language over an alphabet wit ..."
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Consider the following kinds of sets { the set of all possible distances between two vertices of a directed graph. { any set of integers that is either nite or periodic for all n greater or equal to some n0 (such a set is called ultimately periodic). { a context free language over an alphabet with one letter (such a language is also regular). { the set of all possible lengths of words of a context free language. All these sets are isomorphic relatively to the operations of union (or sum), concatenation and Kleene (or transitive) closure. Furthermore, they all share a particularly important property which is not valid in some similar algebraic structures  the concatenation is commutative. The purpose of this paper is to investigate the representation and properties of these sets and also the algorithms to compute the operations mentioned above. The concepts of linear number and {sum are developed in order to provide convenient methods of representation and manipulation. It should...
Theory and Algorithms for Modern Problems in Machine Learning and an Analysis of Markets
, 2008
"... ..."
SEMIRING FRAMEWORKS AND ALGORITHMS
"... ABSTRACT We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The sam ..."
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ABSTRACT We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
ii Copyright c○2012
, 2012
"... iii ivI dedicate this thesis to my father Miguel Machado de Simas, my mother Maria de Lurdes de Simas and my wonderful wife Ana Claudia Guerra, who supported me in each step of the way with love and understanding. ..."
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iii ivI dedicate this thesis to my father Miguel Machado de Simas, my mother Maria de Lurdes de Simas and my wonderful wife Ana Claudia Guerra, who supported me in each step of the way with love and understanding.
Journal of Automata, Languages and Combinatorics u (v) w, x–y c ○ OttovonGuerickeUniversität Magdeburg Semiring Frameworks and Algorithms for ShortestDistance Problems
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.