Languages Associated with Crystallographic Symmetry

  • Nataša Jonoska
  • Mile Krajcevski
  • Gregory McColm
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8553)


We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages \(\mathcal{DCL}_d\), d = 0,1,2,…, within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class \(\mathcal{DCL}_d\). Each language in \(\mathcal{DCL}_d\) is an intersection of d languages in \(\mathcal{DCL}_1\). We prove that there is a one-to-one correspondence between sets of walks starting and ending in the same unit of a d-dimensional periodic (di)graph and the class of languages in \(\mathcal{DCL}_d\).


Abelian Group Regular Language Terminal Vertex Quotient Graph Counter Machine 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nataša Jonoska
    • 1
  • Mile Krajcevski
    • 1
  • Gregory McColm
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA

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