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Coverability and multi-scale coverability on infinite pictures

Guilhem Gamard 1 Gwenaël Richomme 1, 2 
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A word is quasiperiodic (or coverable) if it can be covered with occurrences of another finite word, called its quasiperiod. A word is multi-scale quasiperiodic (or multi-scale coverable) if it has infinitely many different quasiperiods. These notions were previously studied in the domains of text algorithms and combinatorics of right infinite words. We extend them to infinite pictures (two-dimensional words). Then we compare the regularity properties (uniform recurrence, uniform frequencies, topological entropy) of quasiperiodicity with multi-scale quasiperiodicity, and we also compare each of them with its one-dimensional counterpart. We also study which properties of quasiperiods enforce properties on the quasiperiodic words.
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Submitted on : Monday, October 25, 2021 - 10:52:01 AM
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Guilhem Gamard, Gwenaël Richomme. Coverability and multi-scale coverability on infinite pictures. Journal of Computer and System Sciences, Elsevier, 2019, 104, pp.258-277. ⟨10.1016/j.jcss.2017.05.001⟩. ⟨lirmm-01176543⟩



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