15 Search Results for "Day, Joel D."

Document
DOI: 10.4230/LIPIcs.STACS.2026.77
An Improved Version of Hmelevskii’s Theorem on Three-Variable Word Equations

Authors: Aleksi Saarela

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Hmelevskii proved in 1971 that every constant-free three-variable word equation has a parametric solution. We prove an improved version of this result by showing that every such equation has a parametric solution using only three numerical parameters and with only two levels of nesting. This means that the structure of the solution sets of these equations is considerably simpler than has been known before.
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Aleksi Saarela. An Improved Version of Hmelevskii’s Theorem on Three-Variable Word Equations. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{saarela:LIPIcs.STACS.2026.77,
  author =	{Saarela, Aleksi},
  title =	{{An Improved Version of Hmelevskii’s Theorem on Three-Variable Word Equations}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{77:1--77:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.77},
  URN =		{urn:nbn:de:0030-drops-255664},
  doi =		{10.4230/LIPIcs.STACS.2026.77},
  annote =	{Keywords: Combinatorics on words, word equation, parametric word}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.43
Kamp Theorem for Pomset Languages of Higher Dimensional Automata

Authors: Emily Clement, Enzo Erlich, and Jérémy Ledent

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially ordered multisets, or pomsets. Recent work has shown that Monadic Second Order (MSO) logic is as expressive as HDA for pomset languages. In the case of words, Kamp’s theorem states that First Order (FO) logic is as expressive as Linear Temporal Logic (LTL). In this paper, we extend this result to pomsets. To do so, we first investigate the class of pomset languages that are definable in FO. As expected, this is a strict subclass of MSO-definable languages. Then, we define a Linear Temporal Logic for pomsets (LTL_Poms), and show that it is equivalent to FO.
Cite as

Emily Clement, Enzo Erlich, and Jérémy Ledent. Kamp Theorem for Pomset Languages of Higher Dimensional Automata. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 43:1-43:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clement_et_al:LIPIcs.CSL.2026.43,
  author =	{Clement, Emily and Erlich, Enzo and Ledent, J\'{e}r\'{e}my},
  title =	{{Kamp Theorem for Pomset Languages of Higher Dimensional Automata}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{43:1--43:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.43},
  URN =		{urn:nbn:de:0030-drops-254685},
  doi =		{10.4230/LIPIcs.CSL.2026.43},
  annote =	{Keywords: Higher dimensional automata, temporal logic, Kamp’s theorem}
}
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.MFCS.2025.56
Negated String Containment Is Decidable

Authors: Vojtěch Havlena, Michal Hečko, Lukáš Holík, and Ondřej Lengál

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

Abstract
We provide a positive answer to a long-standing open question of the decidability of the not-contains string predicate. Not-contains is practically relevant, for instance in symbolic execution of string manipulating programs. Particularly, we show that the predicate ¬Contains(x₁ … x_n, y₁ … y_m), where x₁ … x_n and y₁ … y_m are sequences of string variables constrained by regular languages, is decidable. Decidability of a not-contains predicate combined with chain-free word equations and regular membership constraints follows.
Cite as

Vojtěch Havlena, Michal Hečko, Lukáš Holík, and Ondřej Lengál. Negated String Containment Is Decidable. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 56:1-56:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{havlena_et_al:LIPIcs.MFCS.2025.56,
  author =	{Havlena, Vojt\v{e}ch and He\v{c}ko, Michal and Hol{\'\i}k, Luk\'{a}\v{s} and Leng\'{a}l, Ond\v{r}ej},
  title =	{{Negated String Containment Is Decidable}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{56:1--56:20},
  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.2025.56},
  URN =		{urn:nbn:de:0030-drops-241631},
  doi =		{10.4230/LIPIcs.MFCS.2025.56},
  annote =	{Keywords: not-contains, string constraints, word combinatorics, primitive word}
}
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.ICDT.2025.29
FC-Datalog as a Framework for Efficient String Querying

Authors: Owen M. Bell, Joel D. Day, and Dominik D. Freydenberger

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Core spanners are a class of document spanners that capture the core functionality of IBM’s AQL. FC is a logic on strings built around word equations that when extended with constraints for regular languages can be seen as a logic for core spanners. The recently introduced FC-Datalog extends FC with recursion, which allows us to define recursive relations for core spanners. Additionally, as FC-Datalog captures 𝖯, it is also a tractable version of Datalog on strings. This presents an opportunity for optimization. We propose a series of FC-Datalog fragments with desirable properties in terms of complexity of model checking, expressive power, and efficiency of checking membership in the fragment. This leads to a range of fragments that all capture LOGSPACE, which we further restrict to obtain linear combined complexity. This gives us a framework to tailor fragments for particular applications. To showcase this, we simulate deterministic regex in a tailored fragment of FC-Datalog.
Cite as

Owen M. Bell, Joel D. Day, and Dominik D. Freydenberger. FC-Datalog as a Framework for Efficient String Querying. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bell_et_al:LIPIcs.ICDT.2025.29,
  author =	{Bell, Owen M. and Day, Joel D. and Freydenberger, Dominik D.},
  title =	{{FC-Datalog as a Framework for Efficient String Querying}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.29},
  URN =		{urn:nbn:de:0030-drops-229708},
  doi =		{10.4230/LIPIcs.ICDT.2025.29},
  annote =	{Keywords: Information extraction, word equations, datalog, document spanners, regex}
}
Document
Position
DOI: 10.4230/TGDK.1.1.5
Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities

Authors: Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
The term life sciences refers to the disciplines that study living organisms and life processes, and include chemistry, biology, medicine, and a range of other related disciplines. Research efforts in life sciences are heavily data-driven, as they produce and consume vast amounts of scientific data, much of which is intrinsically relational and graph-structured. The volume of data and the complexity of scientific concepts and relations referred to therein promote the application of advanced knowledge-driven technologies for managing and interpreting data, with the ultimate aim to advance scientific discovery. In this survey and position paper, we discuss recent developments and advances in the use of graph-based technologies in life sciences and set out a vision for how these technologies will impact these fields into the future. We focus on three broad topics: the construction and management of Knowledge Graphs (KGs), the use of KGs and associated technologies in the discovery of new knowledge, and the use of KGs in artificial intelligence applications to support explanations (explainable AI). We select a few exemplary use cases for each topic, discuss the challenges and open research questions within these topics, and conclude with a perspective and outlook that summarizes the overarching challenges and their potential solutions as a guide for future research.
Cite as

Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma. Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 5:1-5:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{chen_et_al:TGDK.1.1.5,
  author =	{Chen, Jiaoyan and Dong, Hang and Hastings, Janna and Jim\'{e}nez-Ruiz, Ernesto and L\'{o}pez, Vanessa and Monnin, Pierre and Pesquita, Catia and \v{S}koda, Petr and Tamma, Valentina},
  title =	{{Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:33},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.5},
  URN =		{urn:nbn:de:0030-drops-194791},
  doi =		{10.4230/TGDK.1.1.5},
  annote =	{Keywords: Knowledge graphs, Life science, Knowledge discovery, Explainable AI}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.64
Subsequences with Gap Constraints: Complexity Bounds for Matching and Analysis Problems

Authors: Joel D. Day, Maria Kosche, Florin Manea, and Markus L. Schmid

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

Abstract
We consider subsequences with gap constraints, i. e., length-k subsequences p that can be embedded into a string w such that the induced gaps (i. e., the factors of w between the positions to which p is mapped to) satisfy given gap constraints gc = (C_1, C_2, …, C_{k-1}); we call p a gc-subsequence of w. In the case where the gap constraints gc are defined by lower and upper length bounds C_i = (L^-_i, L^+_i) ∈ ℕ² and/or regular languages C_i ∈ REG, we prove tight (conditional on the orthogonal vectors (OV) hypothesis) complexity bounds for checking whether a given p is a gc-subsequence of a string w. We also consider the whole set of all gc-subsequences of a string, and investigate the complexity of the universality, equivalence and containment problems for these sets of gc-subsequences.
Cite as

Joel D. Day, Maria Kosche, Florin Manea, and Markus L. Schmid. Subsequences with Gap Constraints: Complexity Bounds for Matching and Analysis Problems. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 64:1-64:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{day_et_al:LIPIcs.ISAAC.2022.64,
  author =	{Day, Joel D. and Kosche, Maria and Manea, Florin and Schmid, Markus L.},
  title =	{{Subsequences with Gap Constraints: Complexity Bounds for Matching and Analysis Problems}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{64:1--64:18},
  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.2022.64},
  URN =		{urn:nbn:de:0030-drops-173493},
  doi =		{10.4230/LIPIcs.ISAAC.2022.64},
  annote =	{Keywords: String algorithms, subsequences with gap constraints, pattern matching, fine-grained complexity, conditional lower bounds, parameterised complexity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.130
The Theory of Concatenation over Finite Models

Authors: Dominik D. Freydenberger and Liat Peterfreund

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast to it, its semantics are defined to only allow finite models, by limiting the universe to a word and all its factors. As a consequence of this, FC has many of the desirable properties of FO on finite models, while being far more expressive than FO[<]. Most noteworthy among these desirable properties are sufficient criteria for efficient model checking, and capturing various complexity classes by adding operators for transitive closures or fixed points. Not only does FC allow us to obtain new insights and techniques for expressive power and efficient evaluation of document spanners, but it also provides a general framework for logic on words that also has potential applications in other areas.
Cite as

Dominik D. Freydenberger and Liat Peterfreund. The Theory of Concatenation over Finite Models. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 130:1-130:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{freydenberger_et_al:LIPIcs.ICALP.2021.130,
  author =	{Freydenberger, Dominik D. and Peterfreund, Liat},
  title =	{{The Theory of Concatenation over Finite Models}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{130:1--130:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.130},
  URN =		{urn:nbn:de:0030-drops-141997},
  doi =		{10.4230/LIPIcs.ICALP.2021.130},
  annote =	{Keywords: finite model theory, word equations, descriptive complexity, model checking, document spanners}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.25
The Edit Distance to k-Subsequence Universality

Authors: Joel D. Day, Pamela Fleischmann, Maria Kosche, Tore Koß, Florin Manea, and Stefan Siemer

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
A word u is a subsequence of another word w if u can be obtained from w by deleting some of its letters. In the early 1970s, Imre Simon defined the relation ∼_k (called now Simon-Congruence) as follows: two words having exactly the same set of subsequences of length at most k are ∼_k-congruent. This relation was central in defining and analysing piecewise testable languages, but has found many applications in areas such as algorithmic learning theory, databases theory, or computational linguistics. Recently, it was shown that testing whether two words are ∼_k-congruent can be done in optimal linear time. Thus, it is a natural next step to ask, for two words w and u which are not ∼_k-equivalent, what is the minimal number of edit operations that we need to perform on w in order to obtain a word which is ∼_k-equivalent to u. In this paper, we consider this problem in a setting which seems interesting: when u is a k-subsequence universal word. A word u with alph(u) = Σ is called k-subsequence universal if the set of subsequences of length k of u contains all possible words of length k over Σ. As such, our results are a series of efficient algorithms computing the edit distance from w to the language of k-subsequence universal words.
Cite as

Joel D. Day, Pamela Fleischmann, Maria Kosche, Tore Koß, Florin Manea, and Stefan Siemer. The Edit Distance to k-Subsequence Universality. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{day_et_al:LIPIcs.STACS.2021.25,
  author =	{Day, Joel D. and Fleischmann, Pamela and Kosche, Maria and Ko{\ss}, Tore and Manea, Florin and Siemer, Stefan},
  title =	{{The Edit Distance to k-Subsequence Universality}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.25},
  URN =		{urn:nbn:de:0030-drops-136705},
  doi =		{10.4230/LIPIcs.STACS.2021.25},
  annote =	{Keywords: Subsequence, Scattered factor, Subword, Universality, k-subsequence universality, Edit distance, Efficient algorithms}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.124
On the Structure of Solution Sets to Regular Word Equations

Authors: Joel D. Day and Florin Manea

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
For quadratic word equations, there exists an algorithm based on rewriting rules which generates a directed graph describing all solutions to the equation. For regular word equations - those for which each variable occurs at most once on each side of the equation - we investigate the properties of this graph, such as bounds on its diameter, size, and DAG-width, as well as providing some insights into symmetries in its structure. As a consequence, we obtain a combinatorial proof that the problem of deciding whether a regular word equation has a solution is in NP.
Cite as

Joel D. Day and Florin Manea. On the Structure of Solution Sets to Regular Word Equations. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 124:1-124:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{day_et_al:LIPIcs.ICALP.2020.124,
  author =	{Day, Joel D. and Manea, Florin},
  title =	{{On the Structure of Solution Sets to Regular Word Equations}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{124:1--124:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.124},
  URN =		{urn:nbn:de:0030-drops-125314},
  doi =		{10.4230/LIPIcs.ICALP.2020.124},
  annote =	{Keywords: Quadratic Word Equations, Regular Word Equations, String Solving, NP}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.44
Upper Bounds on the Length of Minimal Solutions to Certain Quadratic Word Equations

Authors: Joel D. Day, Florin Manea, and Dirk Nowotka

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
It is a long standing conjecture that the problem of deciding whether a quadratic word equation has a solution is in NP. It has also been conjectured that the length of a minimal solution to a quadratic equation is at most exponential in the length of the equation, with the latter conjecture implying the former. We show that both conjectures hold for some natural subclasses of quadratic equations, namely the classes of regular-reversed, k-ordered, and variable-sparse quadratic equations. We also discuss a connection of our techniques to the topic of unavoidable patterns, and the possibility of exploiting this connection to produce further similar results.
Cite as

Joel D. Day, Florin Manea, and Dirk Nowotka. Upper Bounds on the Length of Minimal Solutions to Certain Quadratic Word Equations. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{day_et_al:LIPIcs.MFCS.2019.44,
  author =	{Day, Joel D. and Manea, Florin and Nowotka, Dirk},
  title =	{{Upper Bounds on the Length of Minimal Solutions to Certain Quadratic Word Equations}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.44},
  URN =		{urn:nbn:de:0030-drops-109889},
  doi =		{10.4230/LIPIcs.MFCS.2019.44},
  annote =	{Keywords: Quadratic Word Equations, Length Upper Bounds, NP, Unavoidable Patterns}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.109
Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Katrin Casel, Joel D. Day, Pamela Fleischmann, Tomasz Kociumaka, Florin Manea, and Markus L. Schmid

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two important graph-parameters, cutwidth and pathwidth. These connections allow us to show that computing the locality number is NP-hard but fixed-parameter tractable (when the locality number or the alphabet size is treated as a parameter), and can be approximated with ratio O(sqrt{log{opt}} log n). As a by-product, we also relate cutwidth via the locality number to pathwidth, which is of independent interest, since it improves the best currently known approximation algorithm for cutwidth. In addition to these main results, we also consider the possibility of greedy-based approximation algorithms for the locality number.
Cite as

Katrin Casel, Joel D. Day, Pamela Fleischmann, Tomasz Kociumaka, Florin Manea, and Markus L. Schmid. Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 109:1-109:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{casel_et_al:LIPIcs.ICALP.2019.109,
  author =	{Casel, Katrin and Day, Joel D. and Fleischmann, Pamela and Kociumaka, Tomasz and Manea, Florin and Schmid, Markus L.},
  title =	{{Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{109:1--109:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.109},
  URN =		{urn:nbn:de:0030-drops-106858},
  doi =		{10.4230/LIPIcs.ICALP.2019.109},
  annote =	{Keywords: Graph and String Parameters, NP-Completeness, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2017.24
Local Patterns

Authors: Joel D. Day, Pamela Fleischmann, Florin Manea, and Dirk Nowotka

Published in: LIPIcs, Volume 93, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)

Abstract
A pattern is a word consisting of constants from an alphabet Sigma of terminal symbols and variables from a set X. Given a pattern alpha, the decision-problem whether a given word w may be obtained by substituting the variables in \alpha for words over Sigma is called the matching problem. While this problem is, in general, NP-complete, several classes of patterns for which it can be efficiently solved are already known. We present two new classes of patterns, called k-local, and strongly-nested, and show that the respective matching problems, as well as membership can be solved efficiently for any fixed k.
Cite as

Joel D. Day, Pamela Fleischmann, Florin Manea, and Dirk Nowotka. Local Patterns. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{day_et_al:LIPIcs.FSTTCS.2017.24,
  author =	{Day, Joel D. and Fleischmann, Pamela and Manea, Florin and Nowotka, Dirk},
  title =	{{Local Patterns}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Lokam, Satya and Ramanujam, R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.24},
  URN =		{urn:nbn:de:0030-drops-84013},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.24},
  annote =	{Keywords: Patterns with Variables, Local Patterns, Combinatorial Pattern Matching, Descriptive Patterns}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.18
The Hardness of Solving Simple Word Equations

Authors: Joel D. Day, Florin Manea, and Dirk Nowotka

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both left and right hand sides is preserved (the variables can be, however, separated by potentially distinct constant factors). Surprisingly, we obtain that solving such simple equations, even when the sides contain exactly the same variables, is NP-hard. By considerations regarding the combinatorial structure of the minimal solutions of the more general quadratic equations we obtain that the satisfiability problem for regular-ordered equations is in NP. The complexity of solving such word equations under regular constraints is also settled. Finally, we show that a related class of simple word equations, that generalises one-variable equations, is in P.
Cite as

Joel D. Day, Florin Manea, and Dirk Nowotka. The Hardness of Solving Simple Word Equations. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{day_et_al:LIPIcs.MFCS.2017.18,
  author =	{Day, Joel D. and Manea, Florin and Nowotka, Dirk},
  title =	{{The Hardness of Solving Simple Word Equations}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.18},
  URN =		{urn:nbn:de:0030-drops-81233},
  doi =		{10.4230/LIPIcs.MFCS.2017.18},
  annote =	{Keywords: Word Equations, Regular Patterns, Regular Constraints}
}
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