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Towards a Coalgebraic Chomsky Hierarchy

(Extended Abstract)
  • Sergey Goncharov
  • Stefan Milius
  • Alexandra Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8705)

Abstract

The Chomsky hierarchy plays a prominent role in the foundations of theoretical computer science relating classes of formal languages of primary importance. In this paper we use recent developments on coalgebraic and monad-based semantics to obtain a generic notion of a \(\mathbb{T}\)-automaton, where \(\mathbb{T}\) is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for \(\mathbb{T}\)-automata, and we show by numerous examples that it correctly instantiates for some known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for studying expressivity power of various machine-based models.

Keywords

Turing Machine Regular Expression Formal Power Series Algebraic Theory Reactive Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Sergey Goncharov
  • Stefan Milius
  • Alexandra Silva
    • 1
  1. 1.Centrum Wiskunde & InformaticaRadboud University NijmegenAmsterdamThe Netherlands

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