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29
Efficient computation of the relative entropy of probabilistic automata
 In LATIN’06, LNCS 3887
, 2006
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Generalizing matrix multiplication for efficient computations on modern computers
 In PPAM
, 2011
"... Abstract. Recent advances in computing allow taking new look at matrix multiplication, where the key ideas are: decreasing interest in recursion, development of processors with thousands (potentially millions) of processing units, and influences from the Algebraic Path Problems. In this context, w ..."
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Abstract. Recent advances in computing allow taking new look at matrix multiplication, where the key ideas are: decreasing interest in recursion, development of processors with thousands (potentially millions) of processing units, and influences from the Algebraic Path Problems. In this context, we propose a generalized matrixmatrix multiplyadd (MMA) operation and illustrate its usability. Furthermore, we elaborate the interrelation between this generalization and the BLAS standard.
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.
Theory and Algorithms for Modern Problems in Machine Learning and an Analysis of Markets
, 2008
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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...
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.
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...
Algorithms for Algebraic Path Properties in Concurrent Systems of Constant Treewidth Components
"... We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural ..."
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We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the onetime preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the bestknown graph algorithm on the product. In this approach, even the answer