6 Search Results for "Fazekas, Szilárd Zsolt"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.9
Linear Time Subsequence and Supersequence Regex Matching

Authors: Antoine Amarilli, Florin Manea, Tina Ringleb, and Markus L. Schmid

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
It is well-known that checking whether a given string w matches a given regular expression r can be done in quadratic time O(|w|⋅ |r|) and that this cannot be improved to a truly subquadratic running time of O((|w|⋅ |r|)^{1-ε}) assuming the strong exponential time hypothesis (SETH). We study a different matching paradigm where we ask instead whether w has a subsequence that matches r, and show that regex matching in this sense can be solved in linear time O(|w| + |r|). Further, the same holds if we ask for a supersequence. We show that the quantitative variants where we want to compute a longest or shortest subsequence or supersequence of w that matches r can be solved in O(|w|⋅ |r|), i. e., asymptotically no worse than classical regex matching; and we show that O(|w| + |r|) is conditionally not possible for these problems. We also investigate these questions with respect to other natural string relations like the infix, prefix, left-extension or extension relation instead of the subsequence and supersequence relation. We further study the complexity of the universal problem where we ask if all subsequences (or supersequences, infixes, prefixes, left-extensions or extensions) of an input string satisfy a given regular expression.
Cite as

Antoine Amarilli, Florin Manea, Tina Ringleb, and Markus L. Schmid. Linear Time Subsequence and Supersequence Regex Matching. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amarilli_et_al:LIPIcs.MFCS.2025.9,
  author =	{Amarilli, Antoine and Manea, Florin and Ringleb, Tina and Schmid, Markus L.},
  title =	{{Linear Time Subsequence and Supersequence Regex Matching}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.9},
  URN =		{urn:nbn:de:0030-drops-241162},
  doi =		{10.4230/LIPIcs.MFCS.2025.9},
  annote =	{Keywords: subsequence, supersequence, regular language, regular expression, automata}
}
Document
DOI: 10.4230/LIPIcs.DNA.31.5
Programmable Co‑Transcriptional Splicing: Realizing Regular Languages via Hairpin Deletion

Authors: Da-Jung Cho, Szilárd Zsolt Fazekas, Shinnosuke Seki, and Max Wiedenhöft

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

Abstract
RNA co-transcriptionality, where RNA is spliced or folded during transcription from DNA templates, offers promising potential for molecular programming. It enables programmable folding of nanoscale RNA structures and has recently been shown to be Turing universal. While post-transcriptional splicing is well studied, co-transcriptional splicing is gaining attention for its efficiency, though its unpredictability still remains a challenge. In this paper, we focus on engineering co-transcriptional splicing, not only as a natural phenomenon but as a programmable mechanism for generating specific RNA target sequences from DNA templates. The problem we address is whether we can encode a set of RNA sequences for a given system onto a DNA template word, ensuring that all the sequences are generated through co-transcriptional splicing. Given that finding the optimal encoding has been shown to be NP-complete under the various energy models considered [Da-Jung Cho et al., 2025], we propose a practical alternative approach under the logarithmic energy model. More specifically, we provide a construction that encodes an arbitrary nondeterministic finite automaton (NFA) into a circular DNA template from which co-transcriptional splicing produces all sequences accepted by the NFA. As all finite languages can be efficiently encoded as NFA, this framework solves the problem of finding small DNA templates for arbitrary target sets of RNA sequences. The quest to obtain the smallest possible such templates naturally leads us to consider the problem of minimizing NFAs and certain practically motivated variants of it, but as we show, those minimization problems are computationally intractable.
Cite as

Da-Jung Cho, Szilárd Zsolt Fazekas, Shinnosuke Seki, and Max Wiedenhöft. Programmable Co‑Transcriptional Splicing: Realizing Regular Languages via Hairpin Deletion. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cho_et_al:LIPIcs.DNA.31.5,
  author =	{Cho, Da-Jung and Fazekas, Szil\'{a}rd Zsolt and Seki, Shinnosuke and Wiedenh\"{o}ft, Max},
  title =	{{Programmable Co‑Transcriptional Splicing: Realizing Regular Languages via Hairpin Deletion}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.5},
  URN =		{urn:nbn:de:0030-drops-238548},
  doi =		{10.4230/LIPIcs.DNA.31.5},
  annote =	{Keywords: RNA Transcription, Co-Transcriptional Splicing, Finite Automata Simulation, NFA Minimization}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.146
Saturation Problems for Families of Automata

Authors: León Bohn, Yong Li, Christof Löding, and Sven Schewe

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Families of deterministic finite automata (FDFA) represent regular ω-languages through their ultimately periodic words (UP-words). An FDFA accepts pairs of words, where the first component corresponds to a prefix of the UP-word, and the second component represents a period of that UP-word. An FDFA is termed saturated if, for each UP-word, either all or none of the pairs representing that UP-word are accepted. We demonstrate that determining whether a given FDFA is saturated can be accomplished in polynomial time, thus improving the known PSPACE upper bound by an exponential. We illustrate the application of this result by presenting the first polynomial learning algorithms for representations of the class of all regular ω-languages. Furthermore, we establish that deciding a weaker property, referred to as almost saturation, is PSPACE-complete. Since FDFAs do not necessarily define regular ω-languages when they are not saturated, we also address the regularity problem and show that it is PSPACE-complete. Finally, we explore a variant of FDFAs called families of deterministic weak automata (FDWA), where the semantics for the periodic part of the UP-word considers ω-words instead of finite words. We demonstrate that saturation for FDWAs is also decidable in polynomial time, that FDWAs always define regular ω-languages, and we compare the succinctness of these different models.
Cite as

León Bohn, Yong Li, Christof Löding, and Sven Schewe. Saturation Problems for Families of Automata. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 146:1-146:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bohn_et_al:LIPIcs.ICALP.2025.146,
  author =	{Bohn, Le\'{o}n and Li, Yong and L\"{o}ding, Christof and Schewe, Sven},
  title =	{{Saturation Problems for Families of Automata}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{146:1--146:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.146},
  URN =		{urn:nbn:de:0030-drops-235239},
  doi =		{10.4230/LIPIcs.ICALP.2025.146},
  annote =	{Keywords: Families of Automata, automata learning, FDFAs}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.4
The Equivalence Problem of E-Pattern Languages with Length Constraints Is Undecidable

Authors: Dirk Nowotka and Max Wiedenhöft

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of variables by associating the variables of a pattern with a system (or disjunction of systems) of linear diophantine inequalities. Pattern languages with length constraints contain only words in which all variables are substituted to words with lengths that fulfill such a given set of length constraints. We consider membership, inclusion, and equivalence problems for erasing and non-erasing pattern languages with length constraints. Our main result shows that the erasing equivalence problem - one of the most prominent open problems in the realm of patterns - becomes undecidable if length constraints are allowed in addition to variable equality. Additionally, it is shown that the terminal-free inclusion problem, a prominent problem which has been shown to be undecidable in the binary case for patterns without any constraints, is also generally undecidable for all larger alphabets in this setting. Finally, we also show that considering regular constraints, i.e., associating variables also with regular languages as additional restrictions together with length constraints for valid substitutions, results in undecidability of the non-erasing equivalence problem. This sets a first upper bound on constraints to obtain undecidability in this case, as this problem is trivially decidable in the case of no constraints and as it has unknown decidability if only regular or only length constraints are considered.
Cite as

Dirk Nowotka and Max Wiedenhöft. The Equivalence Problem of E-Pattern Languages with Length Constraints Is Undecidable. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nowotka_et_al:LIPIcs.CPM.2025.4,
  author =	{Nowotka, Dirk and Wiedenh\"{o}ft, Max},
  title =	{{The Equivalence Problem of E-Pattern Languages with Length Constraints Is Undecidable}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.4},
  URN =		{urn:nbn:de:0030-drops-230988},
  doi =		{10.4230/LIPIcs.CPM.2025.4},
  annote =	{Keywords: Patterns, Pattern Languages, Length Constraints, Regular Constraints, Decidability, Undecidability, Membership, Inclusion, Equivalence}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.28
Subsequence Matching and Analysis Problems for Formal Languages

Authors: Szilárd Zsolt Fazekas, Tore Koß, Florin Manea, Robert Mercaş, and Timo Specht

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
In this paper, we study a series of algorithmic problems related to the subsequences occurring in the strings of a given language, under the assumption that this language is succinctly represented by a grammar generating it, or an automaton accepting it. In particular, we focus on the following problems: Given a string w and a language L, does there exist a word of L which has w as subsequence? Do all words of L have w as a subsequence? Given an integer k alongside L, does there exist a word of L which has all strings of length k, over the alphabet of L, as subsequences? Do all words of L have all strings of length k as subsequences? For the last two problems, efficient algorithms were already presented in [Adamson et al., ISAAC 2023] for the case when L is a regular language, and efficient solutions can be easily obtained for the first two problems. We extend that work as follows: we give sufficient conditions on the class of input-languages, under which these problems are decidable; we provide efficient algorithms for all these problems in the case when the input language is context-free; we show that all problems are undecidable for context-sensitive languages. Finally, we provide a series of initial results related to a class of languages that strictly includes the regular languages and is strictly included in the class of context-sensitive languages, but is incomparable to the of class context-free languages; these results deviate significantly from those reported for language-classes from the Chomsky hierarchy.
Cite as

Szilárd Zsolt Fazekas, Tore Koß, Florin Manea, Robert Mercaş, and Timo Specht. Subsequence Matching and Analysis Problems for Formal Languages. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 28:1-28:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fazekas_et_al:LIPIcs.ISAAC.2024.28,
  author =	{Fazekas, Szil\'{a}rd Zsolt and Ko{\ss}, Tore and Manea, Florin and Merca\c{s}, Robert and Specht, Timo},
  title =	{{Subsequence Matching and Analysis Problems for Formal Languages}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{28:1--28:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.28},
  URN =		{urn:nbn:de:0030-drops-221551},
  doi =		{10.4230/LIPIcs.ISAAC.2024.28},
  annote =	{Keywords: Stringology, String Combinatorics, Subsequence, Formal Languages, Context-Free Languages, Context-Sensitive Languages}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.37
On Algorithmic Self-Assembly of Squares by Co-Transcriptional Folding

Authors: Szilárd Zsolt Fazekas, Hwee Kim, Ryuichi Matsuoka, Shinnosuke Seki, and Hinano Takeuchi

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
Algorithms play a primary role in programming an orchestrated self-assembly of shapes into molecules. In this paper, we study the algorithmic self-assembly of squares by RNA co-transcriptional folding in its oritatami model. We formalize the square self-assembly problem in oritatami and propose a universal oritatami transcript made of 939 types of abstract molecules (beads) and of period 1294 that folds deterministically and co-transcriptionally at delay 3 and maximum arity into the n × n square modulo horizontal and vertical scaling factors for all sufficiently large n’s after building a Θ(log n) width "ruler" that measures n upon the seed of size Θ(log n) on which n is encoded in binary.
Cite as

Szilárd Zsolt Fazekas, Hwee Kim, Ryuichi Matsuoka, Shinnosuke Seki, and Hinano Takeuchi. On Algorithmic Self-Assembly of Squares by Co-Transcriptional Folding. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fazekas_et_al:LIPIcs.ISAAC.2022.37,
  author =	{Fazekas, Szil\'{a}rd Zsolt and Kim, Hwee and Matsuoka, Ryuichi and Seki, Shinnosuke and Takeuchi, Hinano},
  title =	{{On Algorithmic Self-Assembly of Squares by Co-Transcriptional Folding}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.37},
  URN =		{urn:nbn:de:0030-drops-173228},
  doi =		{10.4230/LIPIcs.ISAAC.2022.37},
  annote =	{Keywords: Algorithmic molecular self-assembly, Co-transcriptional folding, Oritatami system, Self-assembly of squares}
}
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