Avoiding Overlaps in Pictures

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.
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Marcella Anselmo, Dora Giammarresi, Maria Madonia. Avoiding Overlaps in Pictures. Giovanni Pighizzini; Cezar Câmpeanu. 19th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2017, Milano, Italy. Springer International Publishing, Lecture Notes in Computer Science, LNCS-10316, pp.16-32, 2017, Descriptional Complexity of Formal Systems. 〈10.1007/978-3-319-60252-3_2〉. 〈hal-01657001〉



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