Quotient Operators for Weighted Rational Expressions

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Abstract

Quotients of words play a key role in formal language theory, however they have been rarely studied in the context of weighted rational expressions. We define the left and right quotients of rational series, and introduce corresponding operators for weighted expressions. We generalize an alternative construction of the derived-term (or Antimirov, or equation) automaton, based on expansions, to handle these operators.


Bibtex (lrde.bib)

@InProceedings{	  demaille.17.ictac,
  author	= {Akim Demaille and Thibaud Michaud},
  title		= {Quotient Operators for Weighted Rational Expressions},
  booktitle	= {Proceedings of the Thirteenth International Colloquium on
		  Theoretical Aspects of Computing (ICTAC)},
  year		= 2017,
  publisher	= {Springer},
  series	= {Lecture Notes in Computer Science},
  address	= {Hanoi, Vietnam},
  month		= oct,
  abstract	= {Quotients of words play a key role in formal language
		  theory, however they have been rarely studied in the
		  context of weighted rational expressions. We define the
		  left and right quotients of rational series, and introduce
		  corresponding operators for weighted expressions. We
		  generalize an alternative construction of the derived-term
		  (or Antimirov, or equation) automaton, based on expansions,
		  to handle these operators.},
  note		= {accepted}
}