Search results for "Sturmian"

showing 4 items of 34 documents

On the number of factors of Sturmian words

1991

Abstract We prove that for m ⩾1, card( A m ) = 1+∑ m i =1 ( m − i +1) ϕ ( i ) where A m is the set of factors of length m of all the Sturmian words and ϕ is the Euler function. This result was conjectured by Dulucq and Gouyou-Beauchamps (1987) who proved that this result implies that the language (∪ m ⩾0 A m ) c is inherently ambiguous. We also give a combinatorial version of the Riemann hypothesis.

Set (abstract data type)Euler functionCombinatoricssymbols.namesakeRiemann hypothesisGeneral Computer ScienceSturmian wordsymbolsComputer Science(all)Theoretical Computer ScienceMathematicsTheoretical Computer Science
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Special factors and the combinatorics of suffix and factor automata

2011

AbstractThe suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages LSA and LFA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.

Special factorGeneral Computer ScienceSpecial factorsFactor automatonBüchi automatonω-automatonTheoretical Computer ScienceCombinatoricsDeterministic automatonTwo-way deterministic finite automatonNondeterministic finite automatonComputer Science::Data Structures and AlgorithmsCombinatorics on wordStandard Sturmian wordsMathematicsDiscrete mathematicsCombinatorics on wordsDAWGPushdown automatonComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Nonlinear Sciences::Cellular Automata and Lattice GasesSuffix automatonProbabilistic automatonSuffix automatonComputer Science::Formal Languages and Automata TheoryComputer Science(all)Theoretical Computer Science
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String Attractors and Infinite Words

2022

The notion of string attractor has been introduced by Kempa and Prezza (STOC 2018) in the context of Data Compression and it represents a set of positions of a finite word in which all of its factors can be “attracted”. The smallest size γ∗ of a string attractor for a finite word is a lower bound for several repetitiveness measures associated with the most common compression schemes, including BWT-based and LZ-based compressors. The combinatorial properties of the measure γ∗ have been studied in [Mantaci et al., TCS 2021]. Very recently, a complexity measure, called string attractor profile function, has been introduced for infinite words, by evaluating γ∗ on each prefix. Such a measure has…

String attractorSettore INF/01 - InformaticaFactor complexityMorphismSturmian wordRecurrent wordRepetitiveness measure
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Counting Berg partitions via Sturmian words and substitution tilings

2013

We develop the connection of Berg partitions with special substitution tilings of two tiles. We obtain a new proof that the number of Berg partitions with a fixed connectivity matrix is equal to half of the sum of its entries, [12]. This approach together with the formula of Seebold [10], for the number of substitutions preserving a given Sturmian sequence, shows that all of the combinatorial substitutions can be realized geometrically as Berg partitions. We treat Sturmian tilings as intersection tilings of bi-partitions. Using the symmetries of bi-partitions we obtain geometrically the palindromic properties of Sturmian sequences (Theorem 3) established combinatorially by de Luca and Migno…

substitutionberg partitionstilingssturmian sequencestoral automorphismsmarkov partitions
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