k-universality of regular languages
Date
12/2023Metadata
Show full item recordAbstract
A subsequence of a word w is a word u such that u = w[i1]w[i2] . . . w[ik], for some set of indices 1 ≤ i1 < i2 < · · · < ik ≤ |w|. A word w is k-subsequence universal over an alphabet Σ if every word in Σk appears in w as a subsequence. In this paper, we study the intersection between the set of k-subsequence universal words over some alphabet Σ and regular languages over Σ. We call a regular language L k-∃-subsequence universal if there exists a k-subsequence universal word in L, and k-∀-subsequence universal if every word of L is k-subsequence universal. We give algorithms solving the problems of deciding if a given regular language, represented by a finite automaton recognising it, is k-∃-subsequence universal and, respectively, if it is k-∀-subsequence universal, for a given k. The algorithms are FPT w.r.t. the size of the input alphabet, and their run-time does not depend on k; they run in polynomial time in the number n of states of the input automaton when the size of the input alphabet is O(log n). Moreover, we show that the problem of deciding if a given regular language is k-∃-subsequence universal is NP-complete, when the language is over a large alphabet. Further, we provide algorithms for counting the number of k-subsequence universal words (paths) accepted by a given deterministic (respectively, nondeterministic) finite automaton, and ranking an input word (path) within the set of k-subsequence universal words accepted by a given finite automaton.
Citation
Adamson , D , Fleischmann , P , Huch , A , Koß , T , Manea , F & Nowotka , D 2023 , k-universality of regular languages . in S Iwata & N Kakimura (eds) , 34th International Symposium on Algorithms and Computation, ISAAC 2023 . , 4 , Leibniz International Proceedings in Informatics, LIPIcs , vol. 283 , Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 34th International Symposium on Algorithms and Computation, ISAAC 2023 , Kyoto , Japan , 3/12/23 . https://doi.org/10.4230/LIPIcs.ISAAC.2023.4 conference
Publication
34th International Symposium on Algorithms and Computation, ISAAC 2023
ISSN
1868-8969Type
Conference item
Description
Duncan Adamson’s work was funded by the Leverhulme Trust via the Leverhulme Research Centre for Functional Material Design. Tore Koß’s work was supported by the DFG project number 389613931. Florin Manea’s work was supported by the DFG Heisenberg-project number 466789228.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.