Algebraic properties of substitution on trajectories

  • Authors:

  • Michael Domaratzki;Petr Sosík;Alfonso Rodríguez-Patón

  • Affiliations:

  • Department of Computer Science, University of Manitoba, Winnipeg, MB Canada;Institute of Computer Science, Silesian University Opava, Czech Republic and Facultad de Informatica, UPM, Campus de Montegancedo, Facultad de Informatica Boadilla del Monte, Madrid, Spain;Facultad de Informatica, UPM, Campus de Montegancedo, Facultad de Informatica Boadilla del Monte, Madrid, Spain

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2006

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Abstract

Language operations on trajectories provide a generalization of many common operations such as concatenation, quotient, shuffle and others. A trajectory is a syntactical condition determining positions where an operation is applied. Besides their elegant language-theoretical properties, the operations on trajectories have been used to solve problems in coding theory, bioinformatics and concurrency theory. We focus on algebraic properties of substitution on trajectories. Their characterization in terms of language-theoretical properties of the associated sets of trajectories is given. The transitivity property is of particular interest. Unlike, e.g., shuffle on trajectories, in the case of substitution the transitive closure of a regular set of trajectories is again regular. This result has consequences in the above-mentioned application areas.