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Languages Associated with Crystallographic Symmetry

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Book cover Unconventional Computation and Natural Computation (UCNC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8553))

Abstract

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 \(\mathcal{DCL}_d\).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Nataša Jonoska, Mile Krajcevski & Gregory McColm

Authors
  1. Nataša Jonoska
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  2. Mile Krajcevski
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  3. Gregory McColm
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Editor information

Editors and Affiliations

  1. Santa Barbara College of Engineering, University of California, Santa Barbara, California, USA

    Oscar H. Ibarra

  2. University of Western Ontario, London, Ontario, Canada

    Lila Kari

  3. University of Western Ontario, London, Ontario, Canada

    Steffen Kopecki

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Jonoska, N., Krajcevski, M., McColm, G. (2014). Languages Associated with Crystallographic Symmetry. In: Ibarra, O., Kari, L., Kopecki, S. (eds) Unconventional Computation and Natural Computation. UCNC 2014. Lecture Notes in Computer Science(), vol 8553. Springer, Cham. https://doi.org/10.1007/978-3-319-08123-6_18

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  • DOI: https://doi.org/10.1007/978-3-319-08123-6_18

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08122-9

  • Online ISBN: 978-3-319-08123-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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