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Avoiding Overlaps in Pictures

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Descriptional Complexity of Formal Systems (DCFS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10316))

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Abstract

In string combinatorics, the sets of strings that have no overlaps (i.e. the prefix of one string does not coincide with the suffix of another string) are extensively investigated since they play an important role in the context of string matching and coding. The notion of overlap can be extended naturally to two dimensions; two pictures p and q have an overlap if one can put one corner of p on some position in q in such a way that all symbols in the common positions coincide. A picture with no self-overlaps is called unbordered and it is a generalization in two dimensions of an unbordered (or bifix-free) string.

We study the problem of generating all unbordered pictures of fixed size and present a construction of non-expandable non-overlapping sets of pictures together with some examples.

Partially supported by INdAM-GNCS Project 2017, FARB Project ORSA138754 of University of Salerno and FIR Project 375E90 of University of Catania.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Salerno, Via Giovanni Paolo II, 132-84084, Fisciano, SA, Italy

    Marcella Anselmo

  2. Dipartimento di Matematica, Università Roma “Tor Vergata”, via della Ricerca Scientifica, 00133, Roma, Italy

    Dora Giammarresi

  3. Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125, Catania, Italy

    Maria Madonia

Authors
  1. Marcella Anselmo
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  2. Dora Giammarresi
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  3. Maria Madonia
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Corresponding author

Correspondence to Dora Giammarresi .

Editor information

Editors and Affiliations

  1. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  2. University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada

    Cezar Câmpeanu

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Anselmo, M., Giammarresi, D., Madonia, M. (2017). Avoiding Overlaps in Pictures. In: Pighizzini, G., Câmpeanu, C. (eds) Descriptional Complexity of Formal Systems. DCFS 2017. Lecture Notes in Computer Science(), vol 10316. Springer, Cham. https://doi.org/10.1007/978-3-319-60252-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-60252-3_2

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