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The derivation of online algorithms, with an application to finding palindromes
 Algorithmica
, 1994
"... Abstract. A theory for the derivation of online algorithms is presented. The algorithms are derived in the BirdMeertens calculus for program transformations. This calculus provides a concise functional notation for algorithms, and a few powerful theorems for proving equalities of functions. The th ..."
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Cited by 7 (4 self)
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Abstract. A theory for the derivation of online algorithms is presented. The algorithms are derived in the BirdMeertens calculus for program transformations. This calculus provides a concise functional notation for algorithms, and a few powerful theorems for proving equalities of functions. The theory for the derivation of online algorithms is illustrated with the derivation of an algorithm for finding palindromes. An online lineartime random access machine (RAM) algorithm for finding the longest palindromic substring in a string is derived, For the purpose of finding the longest palindromic substring, all maximal palindromic substrings are computed. The list of maximal palindromes obtained in the computation of the longest palindrome can be used for other purposes such as finding the largest palindromic rectangle in a matrix and finding the shortest partition of a string into palindromes. Key Words. Derivation of online algorithms, Transformational programming, BirdMeertens calcu
An InitialAlgebra Approach to Directed Acyclic Graphs
, 1995
"... . The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying di#erentways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursiv ..."
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Cited by 5 (0 self)
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. The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying di#erentways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursive pattern of computation on those objects, whichisvery helpful for both functional and parallel programming. We showhow to model a particular kind of directed acyclic graph using this initialalgebra approach. Keywords. Graphs, data types, catamorphisms, initial algebras, BirdMeertens Formalism, program derivation. 1 Introduction It is now widely recognized that the traditional adhoc approaches to program construction do not yield reliable software; a more systematic and formal approach is required. One such approach consists of program veri#cationproving after the fact that a given program satis#es its formal speci#cation. This approach turns out to be di#cult to implement, not lea...
The Derivation of a Hierarchy of Algorithms for Pattern Matching on Arrays
 Proceedings ATABLE92, Second international workshop on array structures
, 1992
"... This paper derives a hierarchy of algorithms for pattern matching on arrays in the BirdMeertens calculus for program transformation. In this calculus, both specifications and algorithms are functions, and a few highlevel theorems are used as transformation rules. An algorithm is derived from its s ..."
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Cited by 4 (2 self)
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This paper derives a hierarchy of algorithms for pattern matching on arrays in the BirdMeertens calculus for program transformation. In this calculus, both specifications and algorithms are functions, and a few highlevel theorems are used as transformation rules. An algorithm is derived from its specification by means of a calculation which typically consists of a sequence of equalities, each an instantiation of a highlevel theorem or a definition. Aspects of the BirdMeertens calculus can be found in [4], [5], [9], [14], [15], and [13]. The laws we use in the derivation are derived from the definition of the data type