Nearly k-Universal Words - Investigating a Part of Simon’s Congruence

Fleischmann, Pamela; Huch, Annika; Mayrock, Annika; Nowotka, Dirk

doi:10.1007/978-3-031-13257-5_5

Cited by 6 publications

(2 citation statements)

References 20 publications

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“…On the other hand, XY-links of w include w [3 : 5], w [8 : 11], and w [11 : 14]. A similar factorization scheme was used by Fleischmann et al [6] as well.…”

Section: Arch Factorizationmentioning

confidence: 99%

Simon's congruence pattern matching

Kim,

Ko,

Han

2024

Theoretical Computer Science

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“…On the other hand, XY-links of w include w [3 : 5], w [8 : 11], and w [11 : 14]. A similar factorization scheme was used by Fleischmann et al [6] as well.…”

Section: Arch Factorizationmentioning

confidence: 99%

Simon's congruence pattern matching

Kim,

Ko,

Han

2024

Theoretical Computer Science

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“…For instance, in automata theory, the theory of formal languages, and logics, it is used in connection with piecewise testable languages [66,67,45,46,47], or subword order and downward closures [39,52,51,71,7]. Naturally, subsequences appear in the area of combinatorics and algorithms on words [62,28,54,53,64,58,63,5,26], but they are also used for modelling concurrency [61,65,14], as well as in database theory (especially in connection with event stream processing [3,38,72]). Nevertheless, a series of classical, well-studied, and well-motivated combinatorial and algorithmic problems deal with subsequences.…”

Section: Introductionmentioning

confidence: 99%

Subsequences in Bounded Ranges: Matching and Analysis Problems

Kosche¹,

Koß²,

Manea³

et al. 2022

Preprint

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In this paper, we consider a variant of the classical algorithmic problem of checking whether a given word v is a subsequence of another word w. More precisely, we consider the problem of deciding, given a number p (defining a range-bound) and two words v and w, whether there exists a factor w[i : i + p − 1] (or, in other words, a range of length p) of w having v as subsequence (i. e., v occurs as a subsequence in the bounded range w[i : i + p − 1]). We give matching upper and lower quadratic bounds for the time complexity of this problem. Further, we consider a series of algorithmic problems in this setting, in which, for given integers k, p and a word w, we analyse the set p-Subseq k (w) of all words of length k which occur as subsequence of some factor of length p of w. Among these, we consider the k-universality problem, the k-equivalence problem, as well as problems related to absent subsequences. Surprisingly, unlike the case of the classical model of subsequences in words where such problems have efficient solutions in general, we show that most of these problems become intractable in the new setting when subsequences in bounded ranges are considered. Finally, we provide an example of how some of our results can be applied to subsequence matching problems for circular words.

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