Smith, D. R. Derivation of parallel sorting algorithms. In Parallel Algorithm Derivation and Program Transformation, R. Paige, J. Reif, and R. Wachter, Eds. Kluwer Academic Publishers, New York, 1993, pp. 55--69. Home/Search Document Details and Download
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Towards Semantics of Self-Adaptive Software - Pavlovic (2000) (2 citations) (Correct)
....frameworks, on the basis of the extant speci cation and programming environments. 2. 2 Example: adaptive sorting To give the reader an idea of what a concrete speci cation carrying module looks like, and how it adaptats on the y, we sketch an (over)simpli ed example, based on the material from [23, 24]. We describe how a sorting module can be automatically recon gured in response, say, to the observed distributions of the input data. Suppose that sorting is done by a Divide and Conquer algorithm, e.g. Quicksort, or Mergesort. The idea of the Divide and Conquer sorting is, of course, to ....
....moreover, for each particular state, which additional predicates, besides the theorems of SDC , have been made true by the executed computational steps, viz the substitutions in SDC . The suitable re nements of SDC yield the speci cations SQS of Quicksort and SMS of Mergesort. As explained in [23, 24], taking d(x; y; z) x = y z implies that c(x; y; z) must mean that z is a merge of x and y which yields Mergesort, whereas taking c(x; y; z) x y = z implies that d(x; y; z) must mean that y and z are a partition of x, such that all elements of y are smaller than every element of z ....
D.R. Smith, Derivation of parallel sorting algorithms. In: Parallel Algorithm Derivation and Program Transformation, eds. R. Paige et al. (Kluwer 1993) 55-69
Mechanizing the Development of Software - Smith (1998) (3 citations) Self-citation (Smith) (Correct)
....the choice of a set of 15 standard decomposition operators from a library. The tactic then uses unskolemization on the soundness axioms to derive specifications for the composition operators. This approach allows the derivation of insertion sort, mergesort, and various parallel sorting algorithms [4, 8]. A dual approach is to choose a set of standard composition operators from a library and use the soundness axioms to derive the decomposition operators (leading to selections sort, heapsort, and quicksort) We present the first approach in detail, then sketch the second. Suppose that we choose ....
....definition for C 2 . This spec can be refined either by applying divide and conquer to create one of several possible simple merge operators: the straightforward one is the usual linear time sequential merge [4] an alternate derivation yields the log time parallel merge underlying Batcher s Sort [8]. Another way to synthesize a definition for C 2 is to reduce it to legacy code ; that is, an existing library routine that can satisfy the C 2 requirement specification. This reduction process uses a general mechanism called connections betweeen theories [7] The code generation process uses ....
Smith, D. R. Derivation of parallel sorting algorithms. In Parallel Algorithm Derivation and Program Transformation, R. Paige, J. Reif, and R. Wachter, Eds. Kluwer Academic Publishers, New York, 1993, pp. 55--69.
Mechanizing the Development of Software - Smith (1999) (3 citations) Self-citation (Smith) (Correct)
....the choice of a set of standard decomposition operators from a library. The tactic then uses unskolemization on the soundness axioms to derive specifications for the composition operators. This approach allows the derivation of insertion sort, mergesort, and various parallel sorting algorithms [4, 8]. A dual approach is to choose a set of standard composition operators from a library and use the soundness axioms to derive the decomposition operators (leading to selections sort, heapsort, and quicksort) We present the first approach in detail, then sketch the second. Suppose that we choose ....
....definition for C 2 . This spec can be refined either by applying divide and conquer to create one of several possible simple merge operators: the straightforward one is the usual linear time sequential merge [4] an alternate derivation yields the log time parallel merge underlying Batcher s Sort [8]. Another way to synthesize a definition for C 2 is to reduce it to legacy code ; that is, an existing library routine that can satisfy the C 2 requirement specification. This reduction process uses a general mechanism called connections betweeen theories [7] The code generation process uses ....
Smith, D. R. Derivation of parallel sorting algorithms. In Parallel Algorithm Derivation and Program Transformation, R. Paige, J. Reif, and R. Wachter, Eds. Kluwer Academic Publishers, New York, 1993, pp. 55--69.
Toward a Classification Approach to Design - Smith (1996) (12 citations) Self-citation (Smith) (Correct)
....is based on the choice of a standard decomposition operator from a library. The tactic then uses unskolemization on the soundness axiom to derive a specification for a composition operator. This approach allows the derivation of insertion sort, mergesort, and various parallel sorting algorithms [16, 21]. A dual approach is to choose a simple composition relation and use the Soundness axiom to derive a decomposition operator. Suppose that we choose concatenation as a simple composition relation on the output domain seq(integer) This gives us the partial signature morphism D 7 Gamma bag(S) I ....
Smith, D. R. Derivation of parallel sorting algorithms. In Parallel Algorithm Derivation and Program Transformation, R. Paige, J. Reif, and R. Wachter, Eds. Kluwer Academic Publishers, New York, 1993, pp. 55--69.
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