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17
Generic programming: An introduction
 3rd International Summer School on Advanced Functional Programming
, 1999
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SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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Cited by 72 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
Temporal Structures
, 1990
"... We combine the principles of the FloydWarshallKleene algorithm, enriched categories, and Birkhoff arithmetic, to yield a useful class of algebras of transitive vertexlabeled spaces. The motivating application is a uniform theory of abstract or parametrized time in which to any given notion of tim ..."
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Cited by 30 (21 self)
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We combine the principles of the FloydWarshallKleene algorithm, enriched categories, and Birkhoff arithmetic, to yield a useful class of algebras of transitive vertexlabeled spaces. The motivating application is a uniform theory of abstract or parametrized time in which to any given notion of time there corresponds an algebra of concurrent behaviors and their operations, always the same operations but interpreted automatically and appropriately for that notion of time. An interesting side application is a language for succinctly naming a wide range of datatypes. 1 Introduction Posets, metric spaces, "closed" automata, and categories have in common the notion of a space of points with distances between points. These distances are respectively truth values, reals, languages, and sets. Distances have two facets, logical and metrical. The logical facet is expressed respectively via implications p ! q between truth values, comparisons x y between reals, inclusions L ` M between langua...
Narrative structure of mathematical texts
 In preparation, available at http://www.macs.hw.ac.uk/~mm20
, 2007
"... Abstract. There are many styles for the narrative structure of a mathematical document. Each mathematician has its own conventions and traditions about labeling portions of texts (e.g., chapter, section, theorem or proof) and identifying statements according to their logical importance (e.g., theore ..."
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Cited by 4 (3 self)
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Abstract. There are many styles for the narrative structure of a mathematical document. Each mathematician has its own conventions and traditions about labeling portions of texts (e.g., chapter, section, theorem or proof) and identifying statements according to their logical importance (e.g., theorem is more important than lemma). Such narrative/structuring labels guide the reader’s navigation of the text and form the key components in the reasoning structure of the theory reflected in the text. We present in this paper a method to computerise the narrative structure of a text which includes the relationships between labeled text entities. These labels and relations are input by the user on top of their natural language text. This narrative structure is then automatically analysed to check its consistency. This automatic analysis consists of two phases: (1) checking the correct usage of labels and relations (i.e., that a “proof” justifies a “theorem ” but cannot justify an “axiom”) and (2) checking that the logical precedences in the document are selfconsistent. The development of this method was driven by the experience of computerising a number of mathematical documents (covering different authoring styles). We illustrate how such computerised narrative structure could be used for further manipulations, i.e. to build a skeleton of a formal document in a formal system like Mizar, Coq or Isabelle. 1
Regular Algebra Applied to Language Problems
, 2004
"... Many functions on contextfree languages can be expressed in the form of the least xed point of a function whose de nition mimics the grammar of the given language. Examples include the function returning the length of the shortest word in a language, and the function returning the smallest num ..."
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Cited by 4 (1 self)
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Many functions on contextfree languages can be expressed in the form of the least xed point of a function whose de nition mimics the grammar of the given language. Examples include the function returning the length of the shortest word in a language, and the function returning the smallest number of edit operations required to transform a given word into a word in a language.
Fusion on Languages
, 2000
"... Many functions on contextfree languages can be expressed in the form of the least fixed point of a function whose definition mimics the grammar of the given language. Examples include the function returning the length of the shortest word in a language, and the function returning the smallest numbe ..."
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Cited by 3 (0 self)
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Many functions on contextfree languages can be expressed in the form of the least fixed point of a function whose definition mimics the grammar of the given language. Examples include the function returning the length of the shortest word in a language, and the function returning the smallest number of edit operations required to transform a given word into a word in a language. This paper presents the basic theory that explains when a function on a contextfree language can be de ned in this way. It is shown how the theory can be applied in a methodology for programming the evaluation of such functions.
EventState Duality: The Enriched Case
"... Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), a ..."
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Cited by 3 (0 self)
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Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), and partially ordered information systems.
Modelling UserInitiative in an Automatic Help Desk System
 In Hitoshi Isahara and Qing Ma, editors, Proceedings of the Second Workshop on Natural Language Processing and Neural Networks (NLPNN2001
, 2001
"... In the following we describe the system KoHDaS which is an automatic help desk system in a call center that basically leaves the dialogue initiative with the user as far as (s)he wants. The user's turn circumscribing the problem as a whole is handed to a hierarchy of recurrent plausibilit ..."
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Cited by 2 (1 self)
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In the following we describe the system KoHDaS which is an automatic help desk system in a call center that basically leaves the dialogue initiative with the user as far as (s)he wants. The user's turn circumscribing the problem as a whole is handed to a hierarchy of recurrent plausibility networks which classify the according problem. In the next step the system extracts even only implicitly mentioned task parameters of this problem class from the turn by a graphmatching technique. Remaining or unidentified task parameters required to solve the problem are asked by the system in an ordinary questionanswering manner.