Partial Commutation on Array Languages

  • Thangasamy Kamaraj
  • Durairaj Gnanaraj Thomas
  • H. Geetha
  • T. Kalyani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7655)


Algebraic characterization of recognizable trace languages were studied and the relation of recognizable trace languages to elementary Petri nets were established by using partial commutation as a tool. Motivated by the above studies in string languages, we have extended the notion of partial commutation to two-dimensional array languages and established that if L is local then φ(L) need not be local, where φ is a partial commutation mapping. We have proved that L(φ(θ)) and φ(L(θ)) are not disjoint, where θ is a finite set of 2 ×2 tiles over the alphabet Γ ∪ {#}. We have also considered partial commutation mapping on Siromoney matrix languages and proved some interesting results.


Tiling system Projection Local recognizability Partial commutation and trace languages Siromoney matrix grammar 


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thangasamy Kamaraj
    • 1
  • Durairaj Gnanaraj Thomas
    • 2
  • H. Geetha
    • 3
  • T. Kalyani
    • 3
  1. 1.Department of MathematicsSathyabama UniversityChennaiIndia
  2. 2.Department of MathematicsMadras Christian CollegeChennaiIndia
  3. 3.Department of MathematicsSt. Joseph’s College of EngineeringChennaiIndia

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