Schema for parallel insertion and deletion

  • Authors:

  • Lila Kari;Shinnosuke Seki

  • Affiliations:

  • Department of Computer Science, University of Western Ontario, London, Ontario, Canada;Department of Computer Science, University of Western Ontario, London, Ontario, Canada

  • Venue:
  • DLT'10 Proceedings of the 14th international conference on Developments in language theory
  • Year:
  • 2010

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Abstract

We propose a general framework for parallel insertion/deletion operations based on p-schemata. A p-schema is a set of tuples of words. When being used for parallel insertion of a language into a word, an element of a p-schema specifies how to split the given word into factors between which the insertion of the language will take place. Parallel deletion based on a p-schema is defined as an "inverse" operation of parallel insertion based on the p-schema. Several well-known language operations are particular cases of p-schema-based insertions or deletions: catenation, Kleene star, reverse catenation, sequential insertion, parallel insertion, insertion next to a given letter, contextual insertion, right and left quotient, sequential deletion, parallel deletion. Additional operations that can be defined using p-schemata include contextual parallel insertion, as well as parallel insertion (deletion) of exactly n words, at most n words, an arbitrary number of words. We also consider the decidability and undecidability of existence of solutions of language equations involving p-schema-based parallel insertion/deletion.