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International Conference on Algebraic Informatics

CAI 2011: Algebraic Informatics pp 21–43Cite as

From Grammars and Automata to Algebras and Coalgebras

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6742))

Abstract

The increasing application of notions and results from category theory, especially from algebra and coalgebra, has revealed that any formal software or hardware model is constructor- or destructor-based, a white-box or a black-box model. A highly-structured system may involve both constructor- and destructor-based components. The two model classes and the respective ways of developing them and reasoning about them are dual to each other. Roughly said, algebras generalize the modeling with context-free grammars, word languages and structural induction, while coalgebras generalize the modeling with automata, Kripke structures, streams, process trees and all other state- or object-oriented formalisms. We summarize the basic concepts of co/algebra and illustrate them at a couple of signatures including those used in language or compiler construction like regular expressions or acceptors.

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Authors and Affiliations

  1. Technical University of Dortmund, Germany

    Peter Padawitz

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  1. Peter Padawitz
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  1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Straße 69, 4040, Linz, Austria

    Franz Winkler

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Padawitz, P. (2011). From Grammars and Automata to Algebras and Coalgebras. In: Winkler, F. (eds) Algebraic Informatics. CAI 2011. Lecture Notes in Computer Science, vol 6742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21493-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-21493-6_2

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  • Print ISBN: 978-3-642-21492-9

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