On Arch Factorization and Subword Universality for Words and Compressed Words

Schnoebelen, Philippe; Julien, Veron,

doi:10.1007/978-3-031-33180-0_21

Cited by 3 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The maximal k for which a word w is k-subsequence universal is denoted by the universality index ι(w) = k. This particular class was first studied in [95,97], and is related to the more general problem of fixed-length universality: for a given k and alphabet Σ, is Σ k described/generated/accepted by a mechanism which describes/generates/accepts languages? Such problems were investigated in contexts related to and motivated by formal languages, automata theory, or combinatorics, where the notion of universality is central [17,50,63,106,2,3,152,64].…”

Section: Word Equationsmentioning

confidence: 99%

“…In Definition 2.29 the arches and rest as well as the universality index of w ∈ Σ * is specifically defined for individual a ∈ alph(w) (cf. the arch jumping functions introduced in [152]). That is the arch factorization and universality index for the suffix of w that starts after the first occurrence of a in w. The marginal sequence of a word w is introduced in Definition 2.1.…”

Section: Subsequencesmentioning

confidence: 99%

“…We show that it is sufficient to guess |var(α)| subsequence universality signatures, one for each variable, instead of the actual images of the variables under a substitution h using the following proposition by Schnoebelen and Veron [152].…”

Section: Matchuniv Is In Npmentioning

confidence: 99%

“…Naively, R requires (2 σ ) σ bits because there can be 2 σ choices for each item. Finally, in the framework of our problem, note that K[1] − K[|γ|] ≤ 1 by Schnoebelen and Veron [152], and that the values of K[i] are non-increasing in i. Therefore, we can encode K as a tuple (l, k ′ ) where It remains to design a deterministic polynomial algorithm that tests the validity of the guessed subsequence universality signature.…”

Section: Proposition 53 ([152]mentioning

confidence: 99%

See 3 more Smart Citations

Matching Patterns with Variables in Approximate Settings

Siemer

View full text Add to dashboard Cite

First and foremost, I hereby express my sincere gratitude and thank my supervisor, Florin Manea, for the excellent guidance and support throughout my studies. Florin is very knowledgeable in many areas of theoretical computer science, encouraging and helpful with new research ideas, and a highly cheerful person throughout my entire studies and everyday work. I am very grateful that he is swift in answering requests and always finds time to discuss research.Secondly, I would like to thank my second supervisor, Carsten Damm. I have been working as a Tutor for Carsten since my Bachelor studies and enjoyed taking his advanced courses in theoretical computer science. Carsten also convinced me to pursue doctoral studies with the back then "new" professor at our institute, Florin Manea. Looking back, I am very grateful for all of these things.Further, I express my gratitude towards Jens Grabowski, who advised me very well with all the formal requirements as a member of the thesis advisory committee.I also extend my many thanks to the entire working group. A special thank you goes to Maria Kosche, Tore Koß, and Paul Sarnighausen-Cahn as my future academic siblings, co-authors, and thesis proofreaders. I am thankful for the amicable and relaxed work environment I experienced with the previously mentioned group members and our master students Tina Ringleb, Timo Specht, and Maximilian Winkler, who work on the same floor. Speaking of people working on the same floor, I want to express my deepest gratitude to Henrik Brosenne, whom I closely collaborated with in teaching, as well as Heike Jachinke and Patricia Nitzke, who were always helping us regarding formal problems, such as traveling, room bookings, and much more, making it exceptionally convenient to deal with.

show abstract