Jacob Kornerup. Mapping Powerlists onto Hypercubes. PhD thesis, The University of Texas at Austin, Department of Computer Sciences, 1994. In preparation.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....do not have to be stated explicitly. 31 One of the fundamental problems with the powerlist notation is to devise compilation strategies for mapping programs (written in the powerlist notation) to specific architectures. The architecture that is the closest conceptually is the hypercube. Kornerup[14] has developed certain strategies whereby each parallel step in a program is mapped to a constant number of local operations and communications at a hypercube node. Combinational circuit verification is an area in which the powerlist notation may be fruitfully employed. Adams[1] has proved the ....

Jacob Kornerup. Mapping Powerlists onto Hypercubes. PhD thesis, The University of Texas at Austin, Department of Computer Sciences, 1994. In preparation.

....= 0 iff p = hxi for some x 2 B ffl lgl : p j q) lgl: p 1 q) lgl:p 1 ffl lgl:p 0 iff p = q j r or p = q 1 r for some q; r 2 P 3 ffl h Deltai, j and 1 satisfy the powerlist axioms Misra s powerlists are one example of such a powerlist algebra, which we call the standard model . Kornerup [4] has another example where j and 1 are defined differently, using the Gray code and inverse Gray code permutations. We refer to the standard model to provide an operational interpretation of the functions that we define, though our proofs are entirely within the powerlist algebra and so are valid ....

Jacob Kornerup. Mapping powerlists onto hypercubes. PhD thesis, Department of Computer Sciences, The University of Texas at Austin, 1994. In preparation.

.... constructs ## (## forms a Powerlist by taking elements from two argument Powerlists alternatively) and ( forms a Powerlist by simply concatenating two argument Powerlists) The algorithms represented by Powerlists are then mapped to architectures such as Hypercube by program derivations [50]. However, to the best of our knowledge, only tensor products have been used for synthesizing programs cognizant of memory hierarchies. For example, a method of program synthesis for a single disk system is discussed in [49] However they have not addressed the issues of data distributions on ....

J. Kornerup. Mapping powerlists onto Hypercubes. Ph.D. thesis, The University of Texas at Austin, Department of Computer Science, 1995.

....= 0 iff p = hxi for some x 2 B ffl lgl : p j q) lgl: p 1 q) lgl:p 1 ffl lgl:p 0 iff p = q j r or p = q 1 r for some q; r 2 P ffl h Deltai, j and 1 satisfy the powerlist axioms Misra s powerlists are one example of such a powerlist algebra, which we call the standard model . Kornerup [4] has another example where j and 1 are defined differently, using the Gray code and inverse Gray code permutations. We refer to the standard model to provide an operational interpretation of the functions that we define, though our proofs are entirely within the powerlist algebra and so are valid ....

Jacob Kornerup. Mapping powerlists onto hypercubes. PhD thesis, Department of Computer Sciences, The University of Texas at Austin, 1994. In preparation.

....do not have to be stated explicitly. One of the fundamental problems with the powerlist notation is to devise compilation strategies for mapping programs (written in the powerlist notation) to specific architectures. The architecture that is the closest conceptually is the hypercube. Kornerup[14] has developed certain strategies whereby each parallel step in a program is mapped to a constant number of local operations and communications at a hypercube node. Combinational circuit verification is an area in which the powerlist notation may be fruitfully employed. Adams[1] has proved the ....

Jacob Kornerup. Mapping Powerlists onto Hypercubes. PhD thesis, The University of Texas at Austin, Department of Computer Sciences, 1994. In preparation.

....examples of parallel algorithms expressed as functions over PowerList. We provide a cost calculus that allows us to quantify the time that implementations of the PowerList notation may take on particular parallel architectures and show an efficient mapping of the PowerList operators to hypercubes [Kor94, Kor95] Finally, we study how different sorting algorithms can be expressed in the PowerList notation, focusing on a derivation of the odd even transposition sort [Kor97a, Kor97c] 2.1 Introduction Functional programming languages typically employ lists where the basic constructors (adding or ....

.... for example, we have descriptions of different versions of matrix multiplication: the standard divide and conquer technique, the Strassen algorithm [Str69] and the hypercube algorithm by Dekel, Nassimi and Sahni [DNS81] The latter algorithm is described using an extended version of PowerLists in [Kor94] 5.3 Final Comments The three data structures we presented were useful in expressing parallel computations. Equally important was the use of formal techniques to derive many of these descriptions from their specifications. This was possible because the structures were designed for equational ....

Jacob Kornerup. Mapping powerlists onto hypercubes. Technical Report CS-TR-94-05, University of Texas at Austin, Department of Computer Sciences, August 1994. Available for download as ftp://ftp.cs.utexas.edu/pub/techreports/tr94-05.ps.Z.

....the Gray coded equivalent in terms of the Gray coded . G operator: u . G v) G = v G . G u This operator can be implemented in constant time on the hypercube, since neighboring elements of the list are neighbors on the hypercube under the Gray coded mapping. It can be proven [2] that: G:u) G = G: u ) It can also be proven that j can be implemented efficiently under Gray coding [2] and thus we have shown that under Gray coding the fundamental operators and some derived operators have efficient implementation on the hypercube. From this it does not follow that ....

....This operator can be implemented in constant time on the hypercube, since neighboring elements of the list are neighbors on the hypercube under the Gray coded mapping. It can be proven [2] that: G:u) G = G: u ) It can also be proven that j can be implemented efficiently under Gray coding [2], and thus we have shown that under Gray coding the fundamental operators and some derived operators have efficient implementation on the hypercube. From this it does not follow that all powerlist functions can be implemented as efficiently on a hypercube as on a CREW PRAM. The Gray coding of a ....

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J. Kornerup: "Mapping Powerlists onto Hypercubes", Technical Report TR9405, Department of Computer Sciences, The University of Texas at Austin, 1994.

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Kor94 J. Kornerup: "Mapping Powerlists onto Hypercubes", Technical Report TR 94-05, Dept. of Computer Sciences, The University of Texas at Austin 1994.

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