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A Recursion Removal Theorem  Proof and Applications
, 1999
"... In this paper we briey introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. This theorem includes as special cases the two techniques discussed by Knuth [12] and Bird [7]. We describe some applications of t ..."
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Cited by 11 (8 self)
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In this paper we briey introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. This theorem includes as special cases the two techniques discussed by Knuth [12] and Bird [7]. We describe some applications of the theorem to cascade recursion, binary cascade recursion, Gray codes, the Towers of Hanoi problem, and an inverse engineering problem. 1 Introduction In this paper we briey introduce some of the ideas behind the transformation theory we have developed over the last eight years at Oxford and Durham Universities and describe a recent result: a general recursion removal theorem. We use a Wide Spectrum Language (called WSL), developed in [19,20,21] which includes lowlevel programming constructs and highlevel abstract specications within a single language. Working within a single language means that the proof that a program correctly implements a specication, or that a specication correct...
Recursion Removal/Introduction by Formal Transformation: An Aid to Program Development and Program Comprehension
 Comput. J
, 1999
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A Recursion Removal Theorem
, 1993
"... In this paper we briefly introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. Recursion removal often forms an important step in the systematic development of an algorithm from a formal specification. We us ..."
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Cited by 7 (3 self)
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In this paper we briefly introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. Recursion removal often forms an important step in the systematic development of an algorithm from a formal specification. We use semanticpreserving transformations to carry out such developments and the theorem proves the correctness of many different classes of recursion removal. This theorem includes as special cases the two techniques discussed by Knuth [13] and Bird [7]. We describe some applications of the theorem to cascade recursion, binary cascade recursion, Gray codes, and an inverse engineering problem.
An efficient APSP algorithm
, 2004
"... In many cases, recursion removal improves the efficiency of recursive algorithms, especially algorithms with large formal parameters, such as All Pair Shortest path (APSP) algorithms. In this article, a recursion removal of the Seidel's APSP [14] is presented, and a general method of recursion ..."
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In many cases, recursion removal improves the efficiency of recursive algorithms, especially algorithms with large formal parameters, such as All Pair Shortest path (APSP) algorithms. In this article, a recursion removal of the Seidel's APSP [14] is presented, and a general method of recursion removal, called stack indexation is introduced.
An Optimal Iterative Algorithm for Shortest Path Query
"... In this paper, we present a new optimal hierarchical approach for shortest path finding. We propose iterative algorithms to find a shortest path and to expand this path into the lowest level. We prove the theoretical complexity of our algorithms, which is linear in both time and space. This is the f ..."
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In this paper, we present a new optimal hierarchical approach for shortest path finding. We propose iterative algorithms to find a shortest path and to expand this path into the lowest level. We prove the theoretical complexity of our algorithms, which is linear in both time and space. This is the first iterative (nonrecursive) approach which achieves the optimal lower bound for this problem. Furthermore, the algorithms in our hierarchical approach are simple and present a good potential for parallelization. We also introduce a new algorithm to perform intraregional shortest path queries in the lowest level of a network hierarchy. Our strategy uses a precomputed subsequence of vertices that belong to the shortest path (hybrid path view) while actually computing the whole shortest path. The hybrid algorithm requires ¢¡¤£¦¥ time and space assuming a uniform distribution of vertices, where £ is the total number of vertices in the region. This represents an improvement concerning space, since a path view approach requires ¢¡¤£¨§� © �� ¥ space in the lowest level.