Results 31 to 40 of about 114 (95)
Subword Complexity and k-Synchronization [PDF]
, 2013 We show that the subword complexity function p_x(n), which counts the number of distinct factors of length n of a sequence x, is k-synchronized in the sense of Carpi if x is k-automatic. As an application, we generalize recent results of Goldstein. We give analogous results for the number of distinct factors of length n that are primitive words or ...
Daniel Goc +2 more
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On Minimal Words With Given Subword Complexity [PDF]
The Electronic Journal of Combinatorics, 1998 We prove that the minimal length of a word $S_n$ having the property that it contains exactly $F_{m+2}$ distinct subwords of length $m$ for $1 \leq m \leq n$ is $F_n + F_{n+2}$. Here $F_n$ is the $n$th Fibonacci number defined by $F_1 = F_2 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n > 2$.
Ming-wei Wang, Jeffrey O. Shallit
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The height of piecewise-testable languages and the complexity of the logic of subwords [PDF]
Logical Methods in Computer Science, 2019 The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been investigated in a ...
Prateek Karandikar, Philippe Schnoebelen
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Arithmetical subword complexity of automatic sequences
CoRR, 2023 We fully classify automatic sequences $a$ over a finite alphabet $Ω$ with the property that each word over $Ω$ appears is $a$ along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal possible arithmetical subword complexity.
Jakub Konieczny, Clemens Müllner
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The Maximal Complexity of Quasiperiodic Infinite Words
Axioms, 2021 A quasiperiod of a finite or infinite string is a word whose occurrences cover every part of the string. An infinite string is referred to as quasiperiodic if it has a quasiperiod.
Ludwig Staiger
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Subword Complexity and Decomposition of the Set of Factors [PDF]
, 2014 In this paper we explore a new hierarchy of classes of languages and infinite words and its connection with complexity classes. Namely, we say that a language belongs to the class $L_k$ if it is a subset of the catenation of $k$ languages $S_1\cdots S_k$, where the number of words of length $n$ in each of $S_i$ is bounded by a constant.
Cassaigne, Julien +3 more
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Subword complexes and edge subdivisions [PDF]
Proceedings of the Steklov Institute of Mathematics, 2014 For a finite Coxeter group, a subword complex is a simplicial complex associated with a pair (Q, π), where Q is a word in the alphabet of simple reflections, $π$ is a group element. We discuss the transformations of such a complex induced by braid moves of the word Q.
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Subword complexes in Coxeter groups
Advances in Mathematics, 2004 Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σand an element in Πdetermine a {\em subword complex}, as introduced in our paper on Gröbner geometry of Schubert polynomials (math.AG/0110058). Subword complexes are demonstrated here to be homeomorphic to balls or spheres, and their Hilbert series are shown to reflect combinatorial ...
Knutson, Allen, Miller, Ezra
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On subword complexity functions
Discrete Applied Mathematics, 1984 The author finds a polynomial formula for the subword complexity function of a cyclic language. A characterization of context-free languages with exponential subword complexity is derived by appropriately using the pumping lemma.
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The Subword Complexity of a Two-Parameter Family of Sequences [PDF]
The Electronic Journal of Combinatorics, 2001 We determine the subword complexity of the characteristic functions of a two-parameter family $\{A_n\}_{n=1}^\infty$ of infinite sequences which are associated with the winning strategies for a family of 2-player games. A special case of the family has the form $A_n=\lfloor n\alpha\rfloor$ for all $n\in {\bf Z}_{>0}$, where $\alpha$ is a fixed ...
Aviezri S. Fraenkel +2 more
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