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.

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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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